Properties

Label 374790.dl
Number of curves $6$
Conductor $374790$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("374790.dl1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 374790.dl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
374790.dl1 374790dl5 [1, 0, 0, -8663435, 9814118535] [2] 14745600  
374790.dl2 374790dl4 [1, 0, 0, -812065, -281511283] [2] 7372800  
374790.dl3 374790dl3 [1, 0, 0, -542985, 152407125] [2, 2] 7372800  
374790.dl4 374790dl6 [1, 0, 0, -110535, 388611315] [2] 14745600  
374790.dl5 374790dl2 [1, 0, 0, -62485, -2217775] [2, 2] 3686400  
374790.dl6 374790dl1 [1, 0, 0, 14395, -265023] [2] 1843200 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 374790.dl have rank \(1\).

Modular form 374790.2.a.dl

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} + q^{8} + q^{9} + q^{10} - 4q^{11} + q^{12} - q^{13} + q^{15} + q^{16} + 6q^{17} + q^{18} + 4q^{19} + O(q^{20}) \)

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.