Properties

Label 371943ba
Number of curves $6$
Conductor $371943$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("371943.ba1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 371943ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
371943.ba5 371943ba1 [1, -1, 0, -62478, -8606849] [2] 2359296 \(\Gamma_0(N)\)-optimal
371943.ba4 371943ba2 [1, -1, 0, -1115883, -453354440] [2, 2] 4718592  
371943.ba3 371943ba3 [1, -1, 0, -1232928, -352344605] [2, 2] 9437184  
371943.ba1 371943ba4 [1, -1, 0, -17853318, -29030850959] [2] 9437184  
371943.ba2 371943ba5 [1, -1, 0, -7826463, 8162546494] [2] 18874368  
371943.ba6 371943ba6 [1, -1, 0, 3487887, -2404010804] [2] 18874368  

Rank

sage: E.rank()
 

The elliptic curves in class 371943ba have rank \(1\).

Modular form 371943.2.a.ba

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

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.