Show commands:
SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 12675f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
12675.i1 | 12675f1 | \([1, 1, 1, 50612, 31877906]\) | \(304175/9477\) | \(-446715516533203125\) | \([]\) | \(120960\) | \(2.0667\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 12675f1 has rank \(1\).
Complex multiplication
The elliptic curves in class 12675f do not have complex multiplication.Modular form 12675.2.a.f
sage: E.q_eigenform(10)