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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 493680.t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 493680.t1 | 493680t1 | \([0, -1, 0, 74543099, -238437685715]\) | \(4742986881028096/5287213506825\) | \(-51064720917471320027443200\) | \([]\) | \(101376000\) | \(3.6194\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 493680.t1 has rank \(0\).
Complex multiplication
The elliptic curves in class 493680.t do not have complex multiplication.Modular form 493680.2.a.t
sage: E.q_eigenform(10)