Properties

Label 117670.m
Number of curves $4$
Conductor $117670$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("117670.m1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 117670.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
117670.m1 117670m4 [1, -1, 1, -449983, -116064619] [2] 1126400  
117670.m2 117670m3 [1, -1, 1, -147403, 20392237] [2] 1126400  
117670.m3 117670m2 [1, -1, 1, -29733, -1588519] [2, 2] 563200  
117670.m4 117670m1 [1, -1, 1, 3887, -149583] [2] 281600 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 117670.m have rank \(1\).

Modular form 117670.2.a.m

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

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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.