Show commands:
SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 140679bc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
140679.bb1 | 140679bc1 | \([1, -1, 0, -115845, 26928404]\) | \(-74246873427/92019697\) | \(-213088656616704099\) | \([]\) | \(1078272\) | \(2.0185\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 140679bc1 has rank \(1\).
Complex multiplication
The elliptic curves in class 140679bc do not have complex multiplication.Modular form 140679.2.a.bc
sage: E.q_eigenform(10)