Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 28314.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
28314.j1 | 28314bb1 | \([1, -1, 0, -468, -20696]\) | \(-128667913/2047032\) | \(-180566645688\) | \([]\) | \(31104\) | \(0.84125\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 28314.j1 has rank \(0\).
Complex multiplication
The elliptic curves in class 28314.j do not have complex multiplication.Modular form 28314.2.a.j
sage: E.q_eigenform(10)