Show commands:
SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 257400b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 257400.b1 | 257400b1 | \([0, 0, 0, -1834875, -956660625]\) | \(-149946252744960/24167\) | \(-110110893750000\) | \([]\) | \(3640320\) | \(2.0966\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 257400b1 has rank \(0\).
Complex multiplication
The elliptic curves in class 257400b do not have complex multiplication.Modular form 257400.2.a.b
sage: E.q_eigenform(10)