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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 68970.x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
68970.x1 | 68970z1 | \([1, 0, 1, 1672096, 1505447876]\) | \(2411938489959911/5962401325710\) | \(-1278093676252112130510\) | \([]\) | \(4530240\) | \(2.7338\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 68970.x1 has rank \(0\).
Complex multiplication
The elliptic curves in class 68970.x do not have complex multiplication.Modular form 68970.2.a.x
sage: E.q_eigenform(10)