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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 61710j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
61710.r1 | 61710j1 | \([1, 1, 0, -9571597, 11398786909]\) | \(-72861639994809235116611/36094044206592000\) | \(-48041172838973952000\) | \([]\) | \(4458240\) | \(2.7298\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 61710j1 has rank \(0\).
Complex multiplication
The elliptic curves in class 61710j do not have complex multiplication.Modular form 61710.2.a.j
sage: E.q_eigenform(10)