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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 422370k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
422370.k1 | 422370k1 | \([1, -1, 0, -8190, 3146256]\) | \(-1771561/123500\) | \(-4235611235251500\) | \([]\) | \(2592000\) | \(1.6783\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 422370k1 has rank \(2\).
Complex multiplication
The elliptic curves in class 422370k do not have complex multiplication.Modular form 422370.2.a.k
sage: E.q_eigenform(10)