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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 10192.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
10192.y1 | 10192v1 | \([0, 1, 0, -3613080, 2646827924]\) | \(-10824513276632329/21926008832\) | \(-10565931061559164928\) | \([]\) | \(354816\) | \(2.5373\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 10192.y1 has rank \(1\).
Complex multiplication
The elliptic curves in class 10192.y do not have complex multiplication.Modular form 10192.2.a.y
sage: E.q_eigenform(10)