Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 5610.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5610.j1 | 5610j1 | \([1, 1, 0, -4242, 107316]\) | \(-8444922396903721/253364474880\) | \(-253364474880\) | \([]\) | \(10080\) | \(0.96622\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 5610.j1 has rank \(1\).
Complex multiplication
The elliptic curves in class 5610.j do not have complex multiplication.Modular form 5610.2.a.j
sage: E.q_eigenform(10)