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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 409101o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
409101.o1 | 409101o1 | \([1, 0, 0, -210603, -1511322]\) | \(40962625/23667\) | \(596860628817529923\) | \([]\) | \(4257792\) | \(2.1004\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 409101o1 has rank \(1\).
Complex multiplication
The elliptic curves in class 409101o do not have complex multiplication.Modular form 409101.2.a.o
sage: E.q_eigenform(10)