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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 272832.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
272832.k1 | 272832k1 | \([0, -1, 0, -7317, 33741]\) | \(458752/261\) | \(24651580391424\) | \([]\) | \(709632\) | \(1.2595\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 272832.k1 has rank \(1\).
Complex multiplication
The elliptic curves in class 272832.k do not have complex multiplication.Modular form 272832.2.a.k
sage: E.q_eigenform(10)