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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 8085.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
8085.k1 | 8085d1 | \([0, -1, 1, 26689, -884458]\) | \(17869652393984/13156171875\) | \(-1547810464921875\) | \([]\) | \(37632\) | \(1.6029\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 8085.k1 has rank \(0\).
Complex multiplication
The elliptic curves in class 8085.k do not have complex multiplication.Modular form 8085.2.a.k
sage: E.q_eigenform(10)