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Properties

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

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

Elliptic curves in class 348726z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
348726.z1 348726z1 [1, 0, 1, -458991, 119650594] [2] 2611200 \(\Gamma_0(N)\)-optimal
348726.z2 348726z2 [1, 0, 1, -458231, 120066770] [2] 5222400  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 348726.2.a.z

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