Properties

Label 115920.ed
Number of curves $4$
Conductor $115920$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("ed1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 115920.ed

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.ed1 115920bs4 \([0, 0, 0, -596307, 177236386]\) \(31412749404762436/7455105\) \(5565206062080\) \([4]\) \(688128\) \(1.8243\)  
115920.ed2 115920bs2 \([0, 0, 0, -37407, 2747806]\) \(31018076123344/472410225\) \(88163085830400\) \([2, 2]\) \(344064\) \(1.4777\)  
115920.ed3 115920bs1 \([0, 0, 0, -4602, -53741]\) \(924093773824/427810005\) \(4989975898320\) \([2]\) \(172032\) \(1.1312\) \(\Gamma_0(N)\)-optimal
115920.ed4 115920bs3 \([0, 0, 0, -3387, 7558234]\) \(-5756278756/33056218125\) \(-24676334605440000\) \([2]\) \(688128\) \(1.8243\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 115920.2.a.ed

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