Properties

Label 348726.z
Number of curves $2$
Conductor $348726$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("z1")
 
E.isogeny_class()
 

Elliptic curves in class 348726.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
348726.z1 348726z1 \([1, 0, 1, -458991, 119650594]\) \(1559100313038878875/74219712\) \(509073004608\) \([2]\) \(2611200\) \(1.7239\) \(\Gamma_0(N)\)-optimal
348726.z2 348726z2 \([1, 0, 1, -458231, 120066770]\) \(-1551368419195022875/10758917283912\) \(-73795413650352408\) \([2]\) \(5222400\) \(2.0705\)  

Rank

sage: E.rank()
 

The elliptic curves in class 348726.z have rank \(1\).

Complex multiplication

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

Modular form 348726.2.a.z

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} + q^{7} - q^{8} + q^{9} + 4 q^{11} + q^{12} + 6 q^{13} - q^{14} + q^{16} - 6 q^{17} - q^{18} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.