Properties

Label 35280dx
Number of curves 8
Conductor 35280
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("35280.bp1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 35280dx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
35280.bp8 35280dx1 [0, 0, 0, 10437, -1260182] [2] 110592 \(\Gamma_0(N)\)-optimal
35280.bp6 35280dx2 [0, 0, 0, -130683, -16472918] [2, 2] 221184  
35280.bp7 35280dx3 [0, 0, 0, -95403, 37117402] [2] 331776  
35280.bp5 35280dx4 [0, 0, 0, -483483, 111452362] [2] 442368  
35280.bp4 35280dx5 [0, 0, 0, -2035803, -1118013302] [2] 442368  
35280.bp3 35280dx6 [0, 0, 0, -2353323, 1386901978] [2, 2] 663552  
35280.bp1 35280dx7 [0, 0, 0, -37633323, 88860133978] [2] 1327104  
35280.bp2 35280dx8 [0, 0, 0, -3200043, 299882842] [2] 1327104  

Rank

sage: E.rank()
 

The elliptic curves in class 35280dx have rank \(0\).

Modular form 35280.2.a.bp

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

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.