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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 41650k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 41650.h1 | 41650k1 | \([1, 1, 0, -1096400, -443360000]\) | \(-79290863149681/213248000\) | \(-392006468000000000\) | \([]\) | \(608256\) | \(2.2501\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 41650k1 has rank \(0\).
Complex multiplication
The elliptic curves in class 41650k do not have complex multiplication.Modular form 41650.2.a.k
sage: E.q_eigenform(10)