Properties

Label 35280ff
Number of curves 4
Conductor 35280
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("35280.es1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 35280ff

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
35280.es3 35280ff1 [0, 0, 0, -17787, -865046] [2] 98304 \(\Gamma_0(N)\)-optimal
35280.es2 35280ff2 [0, 0, 0, -53067, 3629626] [2, 2] 196608  
35280.es4 35280ff3 [0, 0, 0, 123333, 22645546] [2] 393216  
35280.es1 35280ff4 [0, 0, 0, -793947, 272272714] [4] 393216  

Rank

sage: E.rank()
 

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

Modular form 35280.2.a.es

sage: E.q_eigenform(10)
 
\( q + q^{5} + 6q^{13} + 2q^{17} - 8q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.