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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 40425s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 40425.a1 | 40425s1 | \([0, -1, 1, 10159742, -12329342082]\) | \(63090423356788736/72214645051395\) | \(-132749699619555786796875\) | \([]\) | \(5031936\) | \(3.1233\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 40425s1 has rank \(0\).
Complex multiplication
The elliptic curves in class 40425s do not have complex multiplication.Modular form 40425.2.a.s
sage: E.q_eigenform(10)