Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("dd1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 115920dd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.k2 115920dd1 \([0, 0, 0, -1313283, 555158018]\) \(83890194895342081/3958384640000\) \(11819673200885760000\) \([2]\) \(2580480\) \(2.4204\) \(\Gamma_0(N)\)-optimal
115920.k1 115920dd2 \([0, 0, 0, -3617283, -1925328382]\) \(1753007192038126081/478174101507200\) \(1427820216314875084800\) \([2]\) \(5160960\) \(2.7670\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 115920.2.a.dd

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

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.