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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 47096.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
47096.k1 | 47096f1 | \([0, 1, 0, -280, -5264]\) | \(-1682/7\) | \(-10139580416\) | \([]\) | \(19680\) | \(0.60514\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 47096.k1 has rank \(1\).
Complex multiplication
The elliptic curves in class 47096.k do not have complex multiplication.Modular form 47096.2.a.k
sage: E.q_eigenform(10)