Properties

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

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 33135.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
33135.k1 33135i1 \([1, 0, 1, -58444, 5433017]\) \(9993948576518041/597871125\) \(1320697315125\) \([]\) \(96768\) \(1.3872\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 33135.k1 has rank \(1\).

Complex multiplication

The elliptic curves in class 33135.k 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