Properties

Label 346560.ev
Number of curves $2$
Conductor $346560$
CM no
Rank $0$
Graph

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

Elliptic curves in class 346560.ev

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
346560.ev1 346560ev2 \([0, -1, 0, -84237665, 297610425825]\) \(781484460931/900\) \(76131579461920358400\) \([2]\) \(28016640\) \(3.0989\)  
346560.ev2 346560ev1 \([0, -1, 0, -5221985, 4730906337]\) \(-186169411/6480\) \(-548147372125826580480\) \([2]\) \(14008320\) \(2.7524\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 346560.ev have rank \(0\).

Complex multiplication

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

Modular form 346560.2.a.ev

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} + 2 q^{7} + q^{9} - 2 q^{13} - q^{15} - 6 q^{17} + O(q^{20})\)  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 LMFDB 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 LMFDB labels.