Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 21780j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
21780.i1 | 21780j1 | \([0, 0, 0, -297242913, -1987239137587]\) | \(-1161633816071508736/10089075234375\) | \(-25225533083923265733750000\) | \([]\) | \(7539840\) | \(3.6988\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 21780j1 has rank \(0\).
Complex multiplication
The elliptic curves in class 21780j do not have complex multiplication.Modular form 21780.2.a.j
sage: E.q_eigenform(10)