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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 80850.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
80850.o1 | 80850c1 | \([1, 1, 0, -888757125, 11274931162125]\) | \(-861923363555648023441/110929177533556800\) | \(-9991947399603527721825000000\) | \([]\) | \(69189120\) | \(4.1061\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 80850.o1 has rank \(1\).
Complex multiplication
The elliptic curves in class 80850.o do not have complex multiplication.Modular form 80850.2.a.o
sage: E.q_eigenform(10)