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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 494018a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 494018.a1 | 494018a1 | \([1, -1, 0, -648691948, 6333219000016]\) | \(2003092024307193/9529458688\) | \(143617235944851608071831552\) | \([]\) | \(538876800\) | \(3.8683\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 494018a1 has rank \(1\).
Complex multiplication
The elliptic curves in class 494018a do not have complex multiplication.Modular form 494018.2.a.a
sage: E.q_eigenform(10)