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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 67270.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
67270.o1 | 67270f1 | \([1, 0, 1, -1369, -17558]\) | \(9514651159/1093750\) | \(32583906250\) | \([]\) | \(60928\) | \(0.74936\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 67270.o1 has rank \(1\).
Complex multiplication
The elliptic curves in class 67270.o do not have complex multiplication.Modular form 67270.2.a.o
sage: E.q_eigenform(10)