Properties

Label 37191.c
Number of curves 2
Conductor 37191
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("37191.c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 37191.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
37191.c1 37191i2 [1, 0, 0, -60663, 5701086] [2] 115200  
37191.c2 37191i1 [1, 0, 0, -1128, 211959] [2] 57600 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 37191.c have rank \(1\).

Modular form 37191.2.a.c

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{3} - q^{4} - q^{6} + 3q^{8} + q^{9} + q^{11} - q^{12} - 2q^{13} - q^{16} - q^{18} - 2q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.