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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 225400a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 225400.a1 | 225400a1 | \([0, 0, 0, 29920625, 1595623180375]\) | \(100718081964000000/37453512751940327\) | \(-1101592080438256882805750000\) | \([]\) | \(169205760\) | \(3.8680\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 225400a1 has rank \(1\).
Complex multiplication
The elliptic curves in class 225400a do not have complex multiplication.Modular form 225400.2.a.a
sage: E.q_eigenform(10)