Show commands:
SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 40310.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
40310.o1 | 40310e1 | \([1, -1, 0, -19765, 1081781]\) | \(-853938369453624489/6762895769600\) | \(-6762895769600\) | \([]\) | \(247936\) | \(1.2902\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 40310.o1 has rank \(1\).
Complex multiplication
The elliptic curves in class 40310.o do not have complex multiplication.Modular form 40310.2.a.o
sage: E.q_eigenform(10)