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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 188760.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
188760.j1 | 188760bg1 | \([0, -1, 0, -2361, -43635]\) | \(-47007837184/316875\) | \(-9815520000\) | \([]\) | \(147456\) | \(0.75222\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 188760.j1 has rank \(1\).
Complex multiplication
The elliptic curves in class 188760.j do not have complex multiplication.Modular form 188760.2.a.j
sage: E.q_eigenform(10)