Properties

Label 348726.k
Number of curves $1$
Conductor $348726$
CM no
Rank $1$

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

Elliptic curves in class 348726.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
348726.k1 348726k1 \([1, 1, 0, -178, -980]\) \(1742943169/27048\) \(9764328\) \([]\) \(138240\) \(0.14235\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 348726.k1 has rank \(1\).

Complex multiplication

The elliptic curves in class 348726.k do not have complex multiplication.

Modular form 348726.2.a.k

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