Properties

Label 134310.k
Number of curves $1$
Conductor $134310$
CM no
Rank $0$

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

Elliptic curves in class 134310.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
134310.k1 134310cv1 \([1, 1, 0, -180413, 37781517]\) \(-44356801009874089/16616716650000\) \(-243285348472650000\) \([]\) \(2211840\) \(2.0460\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 134310.k1 has rank \(0\).

Complex multiplication

The elliptic curves in class 134310.k do not have complex multiplication.

Modular form 134310.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} + 3 q^{7} - q^{8} + q^{9} + q^{10} - q^{12} - q^{13} - 3 q^{14} + q^{15} + q^{16} - 2 q^{17} - q^{18} - 7 q^{19} + O(q^{20})\) Copy content Toggle raw display