Properties

Label 376768cx
Number of curves $2$
Conductor $376768$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("cx1")
 
E.isogeny_class()
 

Elliptic curves in class 376768cx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
376768.cx2 376768cx1 \([0, -1, 0, -512449, 148701633]\) \(-95443993/5887\) \(-917956169754738688\) \([2]\) \(5160960\) \(2.2012\) \(\Gamma_0(N)\)-optimal
376768.cx1 376768cx2 \([0, -1, 0, -8316929, 9234677249]\) \(408023180713/1421\) \(221575627182178304\) \([2]\) \(10321920\) \(2.5477\)  

Rank

sage: E.rank()
 

The elliptic curves in class 376768cx have rank \(0\).

Complex multiplication

The elliptic curves in class 376768cx do not have complex multiplication.

Modular form 376768.2.a.cx

sage: E.q_eigenform(10)
 
\(q + 2 q^{3} - 2 q^{5} + q^{7} + q^{9} - 4 q^{11} + 2 q^{13} - 4 q^{15} - 4 q^{17} + 2 q^{19} + O(q^{20})\) 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.