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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 414736a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 414736.a1 | 414736a1 | \([0, 0, 0, 1373813, 20866405]\) | \(1029037824/596183\) | \(-166132586623273021808\) | \([]\) | \(34062336\) | \(2.5694\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 414736a1 has rank \(1\).
Complex multiplication
The elliptic curves in class 414736a do not have complex multiplication.Modular form 414736.2.a.a
sage: E.q_eigenform(10)