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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 245a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 245.a1 | 245a1 | \([0, 0, 1, -7, 12]\) | \(-110592/125\) | \(-42875\) | \([]\) | \(48\) | \(-0.41676\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 245a1 has rank \(1\).
Complex multiplication
The elliptic curves in class 245a do not have complex multiplication.Modular form 245.2.a.a
sage: E.q_eigenform(10)