Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("cb1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 115920cb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.t1 115920cb1 \([0, 0, 0, -709430643, -3040869636558]\) \(489781415227546051766883/233890092903563264000\) \(18856586029550943130877952000\) \([2]\) \(74317824\) \(4.1194\) \(\Gamma_0(N)\)-optimal
115920.t2 115920cb2 \([0, 0, 0, 2546397837, -23128680192462]\) \(22649115256119592694355357/15973509811739648000000\) \(-1287809407485835229528064000000\) \([2]\) \(148635648\) \(4.4660\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 115920.2.a.cb

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 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.