Properties

Label 346560jg
Number of curves $2$
Conductor $346560$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("346560.jg1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 346560jg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
346560.jg2 346560jg1 [0, 1, 0, -33755425, -104391847105] [2] 37355520 \(\Gamma_0(N)\)-optimal
346560.jg1 346560jg2 [0, 1, 0, -595644705, -5594836757697] [2] 74711040  

Rank

sage: E.rank()
 

The elliptic curves in class 346560jg have rank \(1\).

Modular form 346560.2.a.jg

sage: E.q_eigenform(10)
 
\( q + q^{3} + q^{5} - 2q^{7} + q^{9} - 2q^{13} + q^{15} - 2q^{17} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.