Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("cz1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 115920cz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.q4 115920cz1 \([0, 0, 0, 41526717, 187202684482]\) \(2652277923951208297919/6605028468326400000\) \(-19722509325967137177600000\) \([2]\) \(29491200\) \(3.5375\) \(\Gamma_0(N)\)-optimal
115920.q3 115920cz2 \([0, 0, 0, -348494403, 2091207788098]\) \(1567558142704512417614401/274462175610000000000\) \(819539664976650240000000000\) \([2, 2]\) \(58982400\) \(3.8841\)  
115920.q2 115920cz3 \([0, 0, 0, -1620832323, -23161900780478]\) \(157706830105239346386477121/13650704956054687500000\) \(40760786587500000000000000000\) \([2]\) \(117964800\) \(4.2306\)  
115920.q1 115920cz4 \([0, 0, 0, -5316494403, 149200642988098]\) \(5565604209893236690185614401/229307220930246900000\) \(684707692782182359449600000\) \([2]\) \(117964800\) \(4.2306\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 115920.2.a.cz

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.