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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 207214p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 207214.c1 | 207214p1 | \([1, -1, 0, -5666143, -5189922857]\) | \(427626629571989457/10153486\) | \(477679694091166\) | \([]\) | \(10160640\) | \(2.3378\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 207214p1 has rank \(1\).
Complex multiplication
The elliptic curves in class 207214p do not have complex multiplication.Modular form 207214.2.a.p
sage: E.q_eigenform(10)