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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 257400.be
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 257400.be1 | 257400be1 | \([0, 0, 0, -844275, 298589150]\) | \(-142648759159300/5577\) | \(-2602005120000\) | \([]\) | \(1763328\) | \(1.8721\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 257400.be1 has rank \(1\).
Complex multiplication
The elliptic curves in class 257400.be do not have complex multiplication.Modular form 257400.2.a.be
sage: E.q_eigenform(10)