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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 126350p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 126350.m1 | 126350p1 | \([1, 1, 0, -894565, -269921155]\) | \(67312940590345/12267496528\) | \(14428379545605029200\) | \([]\) | \(3110400\) | \(2.3950\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 126350p1 has rank \(0\).
Complex multiplication
The elliptic curves in class 126350p do not have complex multiplication.Modular form 126350.2.a.p
sage: E.q_eigenform(10)