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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 58835.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
58835.k1 | 58835d1 | \([0, 0, 1, -36734893, -560830904991]\) | \(-408433618944/9886633715\) | \(-132704916080711369514799715\) | \([]\) | \(61296312\) | \(3.6932\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 58835.k1 has rank \(1\).
Complex multiplication
The elliptic curves in class 58835.k do not have complex multiplication.Modular form 58835.2.a.k
sage: E.q_eigenform(10)