Show commands:
SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 55506.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
55506.g1 | 55506e1 | \([1, 1, 0, -13782992, -20317686528]\) | \(-11872994862835724607989/436955947638718464\) | \(-10656918606960704618496\) | \([]\) | \(4327680\) | \(2.9978\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 55506.g1 has rank \(0\).
Complex multiplication
The elliptic curves in class 55506.g do not have complex multiplication.Modular form 55506.2.a.g
sage: E.q_eigenform(10)