Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 700.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
700.j1 | 700j1 | \([0, 0, 0, -1000, 12500]\) | \(-221184/7\) | \(-3500000000\) | \([]\) | \(720\) | \(0.60753\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 700.j1 has rank \(0\).
Complex multiplication
The elliptic curves in class 700.j do not have complex multiplication.Modular form 700.2.a.j
sage: E.q_eigenform(10)