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SageMath
E = EllipticCurve("by1")
E.isogeny_class()
Elliptic curves in class 53361by
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
53361.cg1 | 53361by1 | \([0, 0, 1, 195657, -6277329]\) | \(45056/27\) | \(-496387702582306227\) | \([]\) | \(1197504\) | \(2.0848\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 53361by1 has rank \(0\).
Complex multiplication
The elliptic curves in class 53361by do not have complex multiplication.Modular form 53361.2.a.by
sage: E.q_eigenform(10)