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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 121680.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
121680.k1 | 121680bd1 | \([0, 0, 0, -2557308, -1587648868]\) | \(-934577152/9375\) | \(-18553632103000800000\) | \([]\) | \(3594240\) | \(2.5162\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 121680.k1 has rank \(1\).
Complex multiplication
The elliptic curves in class 121680.k do not have complex multiplication.Modular form 121680.2.a.k
sage: E.q_eigenform(10)