Properties

Label 115920.dr
Number of curves $4$
Conductor $115920$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("dr1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 115920.dr

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.dr1 115920en4 \([0, 0, 0, -6624147, 6562103186]\) \(10765299591712341649/20708625\) \(61835622912000\) \([2]\) \(2162688\) \(2.3279\)  
115920.dr2 115920en2 \([0, 0, 0, -414147, 102461186]\) \(2630872462131649/3645140625\) \(10884331584000000\) \([2, 2]\) \(1081344\) \(1.9814\)  
115920.dr3 115920en3 \([0, 0, 0, -298227, 161047154]\) \(-982374577874929/3183837890625\) \(-9506889000000000000\) \([2]\) \(2162688\) \(2.3279\)  
115920.dr4 115920en1 \([0, 0, 0, -33267, 613874]\) \(1363569097969/734582625\) \(2193451964928000\) \([2]\) \(540672\) \(1.6348\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 115920.2.a.dr

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

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.