Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 400710.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
400710.j1 | 400710j1 | \([1, 1, 0, -527067, 274677669]\) | \(-344192078341441/494724580200\) | \(-23274753727864156200\) | \([]\) | \(9331200\) | \(2.4082\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 400710.j1 has rank \(0\).
Complex multiplication
The elliptic curves in class 400710.j do not have complex multiplication.Modular form 400710.2.a.j
sage: E.q_eigenform(10)