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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 53130k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
53130.k1 | 53130k1 | \([1, 1, 0, 23182, 8829108]\) | \(1377676163129481431/34399384177213440\) | \(-34399384177213440\) | \([]\) | \(705600\) | \(1.8532\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 53130k1 has rank \(0\).
Complex multiplication
The elliptic curves in class 53130k do not have complex multiplication.Modular form 53130.2.a.k
sage: E.q_eigenform(10)