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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 5056k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5056.v1 | 5056k1 | \([0, 0, 0, -556, 3632]\) | \(72511713/20224\) | \(5301600256\) | \([]\) | \(6144\) | \(0.57314\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 5056k1 has rank \(0\).
Complex multiplication
The elliptic curves in class 5056k do not have complex multiplication.Modular form 5056.2.a.k
sage: E.q_eigenform(10)