Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("df1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 115920df

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.e3 115920df1 \([0, 0, 0, -31709163, 68726631962]\) \(1180838681727016392361/692428800000\) \(2067581317939200000\) \([2]\) \(5898240\) \(2.8385\) \(\Gamma_0(N)\)-optimal
115920.e2 115920df2 \([0, 0, 0, -31893483, 67887201818]\) \(1201550658189465626281/28577902500000000\) \(85333159618560000000000\) \([2, 2]\) \(11796480\) \(3.1851\)  
115920.e4 115920df3 \([0, 0, 0, 4106517, 212484801818]\) \(2564821295690373719/6533572090396050000\) \(-19509141724769158963200000\) \([2]\) \(23592960\) \(3.5317\)  
115920.e1 115920df4 \([0, 0, 0, -70842603, -130433927398]\) \(13167998447866683762601/5158996582031250000\) \(15404681250000000000000000\) \([2]\) \(23592960\) \(3.5317\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 115920.2.a.df

sage: E.q_eigenform(10)
 
\(q - q^{5} - q^{7} - 4q^{11} - 2q^{13} + 6q^{17} + O(q^{20})\)  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 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.