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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 33135k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
33135.m1 | 33135k1 | \([1, 0, 1, -129101738, -564588556837]\) | \(9993948576518041/597871125\) | \(14236080744164543551125\) | \([]\) | \(4548096\) | \(3.3122\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 33135k1 has rank \(0\).
Complex multiplication
The elliptic curves in class 33135k do not have complex multiplication.Modular form 33135.2.a.k
sage: E.q_eigenform(10)