Properties

Label 33135k
Number of curves $1$
Conductor $33135$
CM no
Rank $0$

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Show commands: 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)
 
\(q + q^{2} + q^{3} - q^{4} + q^{5} + q^{6} - 3 q^{8} + q^{9} + q^{10} - 5 q^{11} - q^{12} - 4 q^{13} + q^{15} - q^{16} + q^{18} + 3 q^{19} + O(q^{20})\) Copy content Toggle raw display