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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 56550.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
56550.o1 | 56550f1 | \([1, 1, 0, -415, -10235]\) | \(-317367253345/1565810688\) | \(-39145267200\) | \([]\) | \(50544\) | \(0.71700\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 56550.o1 has rank \(0\).
Complex multiplication
The elliptic curves in class 56550.o do not have complex multiplication.Modular form 56550.2.a.o
sage: E.q_eigenform(10)