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SageMath
E = EllipticCurve("eg1")
E.isogeny_class()
Elliptic curves in class 257600.eg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 257600.eg1 | 257600eg1 | \([0, 1, 0, 10222967, 8084056063]\) | \(7384729019637956864/6036585758984375\) | \(-96585372143750000000000\) | \([]\) | \(20643840\) | \(3.0982\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 257600.eg1 has rank \(1\).
Complex multiplication
The elliptic curves in class 257600.eg do not have complex multiplication.Modular form 257600.2.a.eg
sage: E.q_eigenform(10)