Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("cw1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 115920.cw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.cw1 115920cl1 \([0, 0, 0, -78825627, 112624801354]\) \(489781415227546051766883/233890092903563264000\) \(25866373154390868492288000\) \([2]\) \(24772608\) \(3.5701\) \(\Gamma_0(N)\)-optimal
115920.cw2 115920cl2 \([0, 0, 0, 282933093, 856617784906]\) \(22649115256119592694355357/15973509811739648000000\) \(-1766542397099911151616000000\) \([2]\) \(49545216\) \(3.9167\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 115920.2.a.cw

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