Properties

Label 35280fq
Number of curves $6$
Conductor $35280$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("35280.fp1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 35280fq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
35280.fp6 35280fq1 [0, 0, 0, 70413, 10064306] [2] 294912 \(\Gamma_0(N)\)-optimal
35280.fp5 35280fq2 [0, 0, 0, -494067, 104106674] [2, 2] 589824  
35280.fp4 35280fq3 [0, 0, 0, -2610867, -1534719886] [2] 1179648  
35280.fp2 35280fq4 [0, 0, 0, -7408947, 7761644786] [2, 2] 1179648  
35280.fp3 35280fq5 [0, 0, 0, -6915027, 8841057554] [2] 2359296  
35280.fp1 35280fq6 [0, 0, 0, -118540947, 496764671186] [2] 2359296  

Rank

sage: E.rank()
 

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

Modular form 35280.2.a.fp

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.