Show commands:
SageMath
E = EllipticCurve("gr1")
E.isogeny_class()
Elliptic curves in class 110400gr
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
110400.o1 | 110400gr1 | \([0, -1, 0, -133, -1613]\) | \(-262144/1035\) | \(-1035000000\) | \([]\) | \(55296\) | \(0.41521\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 110400gr1 has rank \(1\).
Complex multiplication
The elliptic curves in class 110400gr do not have complex multiplication.Modular form 110400.2.a.gr
sage: E.q_eigenform(10)