Properties

Label 115920.c
Number of curves $2$
Conductor $115920$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 115920.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.c1 115920dg1 \([0, 0, 0, -35283, 2435218]\) \(1626794704081/83462400\) \(249217391001600\) \([2]\) \(589824\) \(1.5203\) \(\Gamma_0(N)\)-optimal
115920.c2 115920dg2 \([0, 0, 0, 22317, 9612178]\) \(411664745519/13605414480\) \(-40625549950648320\) \([2]\) \(1179648\) \(1.8669\)  

Rank

sage: E.rank()
 

The elliptic curves in class 115920.c have rank \(0\).

Complex multiplication

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

Modular form 115920.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{5} - q^{7} - 6q^{11} - 6q^{17} + 8q^{19} + O(q^{20})\)  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 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.