Properties

Label 37026.v
Number of curves $2$
Conductor $37026$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("v1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 37026.v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
37026.v1 37026be1 [1, -1, 1, -213467, -37884085] [2] 368640 \(\Gamma_0(N)\)-optimal
37026.v2 37026be2 [1, -1, 1, -169907, -53827045] [2] 737280  

Rank

sage: E.rank()
 

The elliptic curves in class 37026.v have rank \(0\).

Complex multiplication

The elliptic curves in class 37026.v do not have complex multiplication.

Modular form 37026.2.a.v

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

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.