Properties

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

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Show commands: SageMath
E = EllipticCurve("ex1")
 
E.isogeny_class()
 

Elliptic curves in class 346560ex

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
346560.ex2 346560ex1 \([0, -1, 0, -33755425, 104391847105]\) \(-50284268371/26542080\) \(-2245211636227385673646080\) \([2]\) \(37355520\) \(3.3768\) \(\Gamma_0(N)\)-optimal
346560.ex1 346560ex2 \([0, -1, 0, -595644705, 5594836757697]\) \(276288773643091/41990400\) \(3551994971375356241510400\) \([2]\) \(74711040\) \(3.7233\)  

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 346560ex do not have complex multiplication.

Modular form 346560.2.a.ex

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

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.