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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 21780.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
21780.k1 | 21780l1 | \([0, 0, 0, -702768, -242864908]\) | \(-7929856/675\) | \(-3267368501897491200\) | \([]\) | \(380160\) | \(2.2974\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 21780.k1 has rank \(0\).
Complex multiplication
The elliptic curves in class 21780.k do not have complex multiplication.Modular form 21780.2.a.k
sage: E.q_eigenform(10)