Show commands:
SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 12696.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
12696.d1 | 12696e1 | \([0, -1, 0, -104145464, 409115098764]\) | \(-778918741604594/27\) | \(-4330284242098176\) | \([]\) | \(728640\) | \(2.9473\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 12696.d1 has rank \(0\).
Complex multiplication
The elliptic curves in class 12696.d do not have complex multiplication.Modular form 12696.2.a.d
sage: E.q_eigenform(10)