Properties

Label 37440cb
Number of curves $6$
Conductor $37440$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("37440.eq1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 37440cb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
37440.eq6 37440cb1 [0, 0, 0, 8628, -123536] [2] 98304 \(\Gamma_0(N)\)-optimal
37440.eq5 37440cb2 [0, 0, 0, -37452, -1026704] [2, 2] 196608  
37440.eq3 37440cb3 [0, 0, 0, -325452, 70742896] [2, 2] 393216  
37440.eq2 37440cb4 [0, 0, 0, -486732, -130599056] [2] 393216  
37440.eq4 37440cb5 [0, 0, 0, -66252, 180332656] [2] 786432  
37440.eq1 37440cb6 [0, 0, 0, -5192652, 4554407536] [2] 786432  

Rank

sage: E.rank()
 

The elliptic curves in class 37440cb have rank \(1\).

Modular form 37440.2.a.eq

sage: E.q_eigenform(10)
 
\( q + q^{5} + 4q^{11} - q^{13} + 6q^{17} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.