Properties

Label 37180d
Number of curves 4
Conductor 37180
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("37180.a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 37180d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
37180.a4 37180d1 [0, 1, 0, -7661, 250264] [2] 77760 \(\Gamma_0(N)\)-optimal
37180.a3 37180d2 [0, 1, 0, -16956, -485900] [2] 155520  
37180.a2 37180d3 [0, 1, 0, -75261, -7871876] [2] 233280  
37180.a1 37180d4 [0, 1, 0, -1199956, -506336700] [2] 466560  

Rank

sage: E.rank()
 

The elliptic curves in class 37180d have rank \(1\).

Modular form 37180.2.a.a

sage: E.q_eigenform(10)
 
\( q - 2q^{3} - q^{5} + 4q^{7} + q^{9} + q^{11} + 2q^{15} + 4q^{19} + O(q^{20}) \)

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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.