Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("35280.dn1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 35280fs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
35280.dn7 35280fs1 [0, 0, 0, 1481613, -523061966] [2] 1179648 \(\Gamma_0(N)\)-optimal
35280.dn6 35280fs2 [0, 0, 0, -7550067, -4683053774] [2, 2] 2359296  
35280.dn5 35280fs3 [0, 0, 0, -53272947, 146321329714] [2, 2] 4718592  
35280.dn4 35280fs4 [0, 0, 0, -106334067, -421926912974] [2] 4718592  
35280.dn8 35280fs5 [0, 0, 0, 8960973, 467734632946] [2] 9437184  
35280.dn2 35280fs6 [0, 0, 0, -847072947, 9489188569714] [2, 2] 9437184  
35280.dn3 35280fs7 [0, 0, 0, -841780947, 9613604548114] [2] 18874368  
35280.dn1 35280fs8 [0, 0, 0, -13553164947, 607308275951314] [2] 18874368  

Rank

sage: E.rank()
 

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

Modular form 35280.2.a.dn

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.