Properties

Label 348726c
Number of curves $2$
Conductor $348726$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 348726c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
348726.c1 348726c1 [1, 1, 0, -560612209656, -161523012846271680] [2] 7280824320 \(\Gamma_0(N)\)-optimal
348726.c2 348726c2 [1, 1, 0, -488690381816, -204488005201738944] [2] 14561648640  

Rank

sage: E.rank()
 

The elliptic curves in class 348726c have rank \(0\).

Complex multiplication

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

Modular form 348726.2.a.c

sage: E.q_eigenform(10)
 
\( q - q^{2} - q^{3} + q^{4} - 2q^{5} + q^{6} - q^{7} - q^{8} + q^{9} + 2q^{10} + 6q^{11} - q^{12} - 6q^{13} + q^{14} + 2q^{15} + q^{16} - 2q^{17} - q^{18} + O(q^{20}) \)

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.