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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 493680a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 493680.a1 | 493680a1 | \([0, -1, 0, -3593256, -4830892944]\) | \(-531244194299/736950000\) | \(-7117576400414515200000\) | \([]\) | \(57784320\) | \(2.8855\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 493680a1 has rank \(1\).
Complex multiplication
The elliptic curves in class 493680a do not have complex multiplication.Modular form 493680.2.a.a
sage: E.q_eigenform(10)