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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 67270.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
67270.j1 | 67270g1 | \([1, 1, 0, -1315148, 519117502]\) | \(9514651159/1093750\) | \(28918336738233906250\) | \([]\) | \(1888768\) | \(2.4664\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 67270.j1 has rank \(1\).
Complex multiplication
The elliptic curves in class 67270.j do not have complex multiplication.Modular form 67270.2.a.j
sage: E.q_eigenform(10)