Struct EllipticCurve 

pub struct EllipticCurve {
    pub field: String,
    pub a: i64,
    pub b: i64,
}

An elliptic curve E: y² = x³ + ax + b over a field k.

Fields

field: String

The base field.

a: i64

Coefficient a.

b: i64

Coefficient b.

Implementations

impl EllipticCurve

pub fn new(field: impl Into<String>, a: i64, b: i64) -> Self

Create an elliptic curve y² = x³ + ax + b.

pub fn discriminant(&self) -> i64

Discriminant Δ = -16(4a³ + 27b²). Non-zero iff the curve is non-singular.

pub fn is_non_singular(&self) -> bool

Whether the curve is non-singular (Δ ≠ 0).

pub fn j_invariant(&self) -> Option<f64>

j-invariant j = -1728 * (4a)³ / Δ (simplified for short Weierstrass).

pub fn j_class(&self) -> String

Check if this is an isomorphism class representative (j-invariant determines it over alg. closed).

Trait Implementations

impl Clone for EllipticCurve

fn clone(&self) -> EllipticCurve

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for EllipticCurve

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl Display for EllipticCurve

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.