Show commands:
SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 122694.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
122694.y1 | 122694i1 | \([1, 1, 0, -1453091, 669703533]\) | \(851494303283/5668704\) | \(2258939768811856416\) | \([]\) | \(4181760\) | \(2.3569\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 122694.y1 has rank \(1\).
Complex multiplication
The elliptic curves in class 122694.y do not have complex multiplication.Modular form 122694.2.a.y
sage: E.q_eigenform(10)