Properties

Label 115920cx
Number of curves $2$
Conductor $115920$
CM no
Rank $1$
Graph

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

Elliptic curves in class 115920cx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.b1 115920cx1 \([0, 0, 0, -23695293, 44395733783]\) \(-126142795384287538429696/9315359375\) \(-108654351750000\) \([]\) \(4250880\) \(2.5895\) \(\Gamma_0(N)\)-optimal
115920.b2 115920cx2 \([0, 0, 0, -23456793, 45333186383]\) \(-122372013839654770813696/5297595236711512175\) \(-61791150841003078009200\) \([]\) \(12752640\) \(3.1388\)  

Rank

sage: E.rank()
 

The elliptic curves in class 115920cx have rank \(1\).

Complex multiplication

The elliptic curves in class 115920cx do not have complex multiplication.

Modular form 115920.2.a.cx

sage: E.q_eigenform(10)
 
\(q - q^{5} - q^{7} - 6q^{11} - q^{13} - 6q^{17} - 2q^{19} + O(q^{20})\)  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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.