Properties

Label 115920.da
Number of curves $4$
Conductor $115920$
CM no
Rank $2$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("da1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 115920.da

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.da1 115920ea4 \([0, 0, 0, -409827, 86681954]\) \(2549399737314529/388286718750\) \(1159417929600000000\) \([2]\) \(1572864\) \(2.1900\)  
115920.da2 115920ea2 \([0, 0, 0, -111747, -13055614]\) \(51682540549249/5249002500\) \(15673437480960000\) \([2, 2]\) \(786432\) \(1.8434\)  
115920.da3 115920ea1 \([0, 0, 0, -108867, -13825726]\) \(47788676405569/579600\) \(1730676326400\) \([2]\) \(393216\) \(1.4969\) \(\Gamma_0(N)\)-optimal
115920.da4 115920ea3 \([0, 0, 0, 140253, -63506014]\) \(102181603702751/642612880350\) \(-1918831778919014400\) \([2]\) \(1572864\) \(2.1900\)  

Rank

sage: E.rank()
 

The elliptic curves in class 115920.da have rank \(2\).

Complex multiplication

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

Modular form 115920.2.a.da

sage: E.q_eigenform(10)
 
\(q + q^{5} - q^{7} - 6 q^{13} + 2 q^{17} - 4 q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.