Show commands:
SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 81312.x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
81312.x1 | 81312bh1 | \([0, -1, 0, -6189, 189477]\) | \(52906619392/1701\) | \(843042816\) | \([]\) | \(84480\) | \(0.80752\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 81312.x1 has rank \(0\).
Complex multiplication
The elliptic curves in class 81312.x do not have complex multiplication.Modular form 81312.2.a.x
sage: E.q_eigenform(10)