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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 47775.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
47775.k1 | 47775dc1 | \([0, 1, 1, 572, 6304]\) | \(28672/39\) | \(-28103404875\) | \([]\) | \(46368\) | \(0.69067\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 47775.k1 has rank \(0\).
Complex multiplication
The elliptic curves in class 47775.k do not have complex multiplication.Modular form 47775.2.a.k
sage: E.q_eigenform(10)