Properties

Label 40950.dh
Number of curves 8
Conductor 40950
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("40950.dh1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 40950.dh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
40950.dh1 40950dm8 [1, -1, 1, -9042852380, 330985708384497] [2] 21233664  
40950.dh2 40950dm6 [1, -1, 1, -565178630, 5171750824497] [2, 2] 10616832  
40950.dh3 40950dm7 [1, -1, 1, -558232880, 5305053658497] [2] 21233664  
40950.dh4 40950dm5 [1, -1, 1, -111691130, 453616474497] [2] 7077888  
40950.dh5 40950dm3 [1, -1, 1, -35758130, 78725614497] [2] 5308416  
40950.dh6 40950dm2 [1, -1, 1, -9316130, 1937974497] [2, 2] 3538944  
40950.dh7 40950dm1 [1, -1, 1, -5788130, -5329705503] [2] 1769472 \(\Gamma_0(N)\)-optimal
40950.dh8 40950dm4 [1, -1, 1, 36610870, 15348658497] [2] 7077888  

Rank

sage: E.rank()
 

The elliptic curves in class 40950.dh have rank \(1\).

Modular form 40950.2.a.dh

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{4} - q^{7} + q^{8} - q^{13} - q^{14} + q^{16} + 6q^{17} - 4q^{19} + O(q^{20}) \)

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 LMFDB numbering.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 3 & 4 & 6 & 12 & 12 \\ 2 & 1 & 2 & 6 & 2 & 3 & 6 & 6 \\ 4 & 2 & 1 & 12 & 4 & 6 & 12 & 3 \\ 3 & 6 & 12 & 1 & 12 & 2 & 4 & 4 \\ 4 & 2 & 4 & 12 & 1 & 6 & 3 & 12 \\ 6 & 3 & 6 & 2 & 6 & 1 & 2 & 2 \\ 12 & 6 & 12 & 4 & 3 & 2 & 1 & 4 \\ 12 & 6 & 3 & 4 & 12 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.