Properties

Label 2790.c
Number of curves $6$
Conductor $2790$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("2790.c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2790.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2790.c1 2790g5 [1, -1, 0, -2767680, 1772929620] [2] 32768  
2790.c2 2790g4 [1, -1, 0, -172980, 27734400] [2, 2] 16384  
2790.c3 2790g6 [1, -1, 0, -170280, 28639980] [2] 32768  
2790.c4 2790g3 [1, -1, 0, -33300, -1815264] [2] 16384  
2790.c5 2790g2 [1, -1, 0, -10980, 421200] [2, 2] 8192  
2790.c6 2790g1 [1, -1, 0, 540, 27216] [2] 4096 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 2790.c have rank \(0\).

Modular form 2790.2.a.c

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.