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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 257400.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 257400.k1 | 257400k1 | \([0, 0, 0, 28005, 59642710]\) | \(65077813630/41209568829\) | \(-1538138914628659200\) | \([]\) | \(3732480\) | \(2.1688\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 257400.k1 has rank \(0\).
Complex multiplication
The elliptic curves in class 257400.k do not have complex multiplication.Modular form 257400.2.a.k
sage: E.q_eigenform(10)