Properties

Label 361920.da
Number of curves $4$
Conductor $361920$
CM no
Rank $0$
Graph

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

Elliptic curves in class 361920.da

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
361920.da1 361920da4 \([0, 1, 0, -534561, -137908161]\) \(64443098670429961/6032611833300\) \(1581412996428595200\) \([2]\) \(9437184\) \(2.2305\)  
361920.da2 361920da2 \([0, 1, 0, -118561, 13266239]\) \(703093388853961/115124490000\) \(30179194306560000\) \([2, 2]\) \(4718592\) \(1.8839\)  
361920.da3 361920da1 \([0, 1, 0, -113441, 14668095]\) \(615882348586441/21715200\) \(5692509388800\) \([2]\) \(2359296\) \(1.5373\) \(\Gamma_0(N)\)-optimal
361920.da4 361920da3 \([0, 1, 0, 215519, 74803775]\) \(4223169036960119/11647532812500\) \(-3053330841600000000\) \([2]\) \(9437184\) \(2.2305\)  

Rank

sage: E.rank()
 

The elliptic curves in class 361920.da have rank \(0\).

Complex multiplication

The elliptic curves in class 361920.da do not have complex multiplication.

Modular form 361920.2.a.da

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} - 4 q^{7} + q^{9} + 4 q^{11} - q^{13} - q^{15} - 6 q^{17} + 4 q^{19} + O(q^{20})\) Copy content 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.