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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 76440.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
76440.o1 | 76440c1 | \([0, -1, 0, -329051, -447467040]\) | \(-42717947152384/913520014875\) | \(-84260177524342638000\) | \([]\) | \(2721600\) | \(2.5042\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 76440.o1 has rank \(1\).
Complex multiplication
The elliptic curves in class 76440.o do not have complex multiplication.Modular form 76440.2.a.o
sage: E.q_eigenform(10)