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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 75712.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
75712.o1 | 75712n1 | \([0, 1, 0, -225, -1793]\) | \(-114244/49\) | \(-542703616\) | \([]\) | \(30720\) | \(0.38357\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 75712.o1 has rank \(1\).
Complex multiplication
The elliptic curves in class 75712.o do not have complex multiplication.Modular form 75712.2.a.o
sage: E.q_eigenform(10)