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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 47190.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
47190.s1 | 47190q1 | \([1, 1, 0, 18696918, -27118513836]\) | \(3372036481719478199/3434349802291200\) | \(-736183380581712868147200\) | \([]\) | \(7717248\) | \(3.2665\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 47190.s1 has rank \(1\).
Complex multiplication
The elliptic curves in class 47190.s do not have complex multiplication.Modular form 47190.2.a.s
sage: E.q_eigenform(10)