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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 177744.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
177744.j1 | 177744bk1 | \([0, -1, 0, -4187195992, -104212207336976]\) | \(25311095642246736793/20804234379264\) | \(6673203577884742760911601664\) | \([]\) | \(195858432\) | \(4.2677\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 177744.j1 has rank \(0\).
Complex multiplication
The elliptic curves in class 177744.j do not have complex multiplication.Modular form 177744.2.a.j
sage: E.q_eigenform(10)