Properties

Label 35280fj
Number of curves $2$
Conductor $35280$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("35280.ev1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 35280fj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
35280.ev1 35280fj1 [0, 0, 0, -105987, 5075714] [2] 258048 \(\Gamma_0(N)\)-optimal
35280.ev2 35280fj2 [0, 0, 0, 387933, 38958626] [2] 516096  

Rank

sage: E.rank()
 

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

Modular form 35280.2.a.ev

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.