Properties

Label 35280.do
Number of curves 8
Conductor 35280
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("35280.do1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 35280.do

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
35280.do1 35280fr8 [0, 0, 0, -15241107, 22901972114] [2] 786432  
35280.do2 35280fr6 [0, 0, 0, -952707, 357734594] [2, 2] 393216  
35280.do3 35280fr7 [0, 0, 0, -776307, 494303474] [2] 786432  
35280.do4 35280fr4 [0, 0, 0, -564627, -163301614] [2] 196608  
35280.do5 35280fr3 [0, 0, 0, -70707, 3346994] [2, 2] 196608  
35280.do6 35280fr2 [0, 0, 0, -35427, -2530654] [2, 2] 98304  
35280.do7 35280fr1 [0, 0, 0, -147, -110446] [2] 49152 \(\Gamma_0(N)\)-optimal
35280.do8 35280fr5 [0, 0, 0, 246813, 25128866] [2] 393216  

Rank

sage: E.rank()
 

The elliptic curves in class 35280.do have rank \(1\).

Modular form 35280.2.a.do

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

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.