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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 47610r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
47610.b1 | 47610r1 | \([1, -1, 0, -52470, 819238900]\) | \(-529/9600\) | \(-289919296077601161600\) | \([]\) | \(1978368\) | \(2.6052\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 47610r1 has rank \(1\).
Complex multiplication
The elliptic curves in class 47610r do not have complex multiplication.Modular form 47610.2.a.r
sage: E.q_eigenform(10)