Properties

Label 5445.c
Number of curves 8
Conductor 5445
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("5445.c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 5445.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
5445.c1 5445g7 [1, -1, 1, -2352263, -1388010918] [2] 40960  
5445.c2 5445g5 [1, -1, 1, -147038, -21653508] [2, 2] 20480  
5445.c3 5445g8 [1, -1, 1, -119813, -29940798] [2] 40960  
5445.c4 5445g4 [1, -1, 1, -87143, 9923136] [2] 10240  
5445.c5 5445g3 [1, -1, 1, -10913, -200208] [2, 2] 10240  
5445.c6 5445g2 [1, -1, 1, -5468, 154806] [2, 2] 5120  
5445.c7 5445g1 [1, -1, 1, -23, 6702] [2] 2560 \(\Gamma_0(N)\)-optimal
5445.c8 5445g6 [1, -1, 1, 38092, -1533144] [2] 20480  

Rank

sage: E.rank()
 

The elliptic curves in class 5445.c have rank \(1\).

Modular form 5445.2.a.c

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

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 16 & 4 & 8 & 16 & 8 \\ 2 & 1 & 2 & 8 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 16 & 4 & 8 & 16 & 8 \\ 16 & 8 & 16 & 1 & 4 & 2 & 4 & 8 \\ 4 & 2 & 4 & 4 & 1 & 2 & 4 & 2 \\ 8 & 4 & 8 & 2 & 2 & 1 & 2 & 4 \\ 16 & 8 & 16 & 4 & 4 & 2 & 1 & 8 \\ 8 & 4 & 8 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.