Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 8048.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
8048.j1 | 8048b1 | \([0, 1, 0, -32, 68]\) | \(-3650692/503\) | \(-515072\) | \([]\) | \(640\) | \(-0.17223\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 8048.j1 has rank \(1\).
Complex multiplication
The elliptic curves in class 8048.j do not have complex multiplication.Modular form 8048.2.a.j
sage: E.q_eigenform(10)