Show commands:
SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 111573.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
111573.f1 | 111573e1 | \([0, 0, 1, -1534239, 1592795188]\) | \(-52367109451776/113395848049\) | \(-864851051156600858427\) | \([]\) | \(5246976\) | \(2.7063\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 111573.f1 has rank \(0\).
Complex multiplication
The elliptic curves in class 111573.f do not have complex multiplication.Modular form 111573.2.a.f
sage: E.q_eigenform(10)