Properties

Label 7935.d
Number of curves 8
Conductor 7935
CM no
Rank 0
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath

sage: E = EllipticCurve("7935.d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7935.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7935.d1 7935b7 [1, 1, 1, -1142651, 469654508] [2] 50688  
7935.d2 7935b5 [1, 1, 1, -71426, 7313798] [2, 2] 25344  
7935.d3 7935b8 [1, 1, 1, -58201, 10122788] [2] 50688  
7935.d4 7935b3 [1, 1, 1, -42331, -3369886] [2] 12672  
7935.d5 7935b4 [1, 1, 1, -5301, 66498] [2, 2] 12672  
7935.d6 7935b2 [1, 1, 1, -2656, -53056] [2, 2] 6336  
7935.d7 7935b1 [1, 1, 1, -11, -2272] [2] 3168 \(\Gamma_0(N)\)-optimal
7935.d8 7935b6 [1, 1, 1, 18504, 523554] [2] 25344  

Rank

sage: E.rank()
 

The elliptic curves in class 7935.d have rank \(0\).

Modular form 7935.2.a.d

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.