Properties

Label 35280el
Number of curves $4$
Conductor $35280$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("35280.cv1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 35280el

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
35280.cv4 35280el1 [0, 0, 0, 16317, 1278018] [2] 147456 \(\Gamma_0(N)\)-optimal
35280.cv3 35280el2 [0, 0, 0, -124803, 13724802] [2, 2] 294912  
35280.cv2 35280el3 [0, 0, 0, -618723, -175051422] [2] 589824  
35280.cv1 35280el4 [0, 0, 0, -1888803, 999095202] [2] 589824  

Rank

sage: E.rank()
 

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

Modular form 35280.2.a.cv

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.