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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 12870a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 12870.a1 | 12870a1 | \([1, -1, 0, -11895, -498979]\) | \(-9456845543523/57200000\) | \(-1125867600000\) | \([]\) | \(33600\) | \(1.1519\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 12870a1 has rank \(0\).
Complex multiplication
The elliptic curves in class 12870a do not have complex multiplication.Modular form 12870.2.a.a
sage: E.q_eigenform(10)