Properties

Label 115920r
Number of curves $4$
Conductor $115920$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("r1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 115920r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.s4 115920r1 \([0, 0, 0, 13497, 659878]\) \(1457028215984/1851148215\) \(-345468684476160\) \([2]\) \(393216\) \(1.4756\) \(\Gamma_0(N)\)-optimal
115920.s3 115920r2 \([0, 0, 0, -81723, 6392122]\) \(80859142234084/23148101025\) \(17279964822758400\) \([2, 2]\) \(786432\) \(1.8222\)  
115920.s2 115920r3 \([0, 0, 0, -487443, -125953742]\) \(8579021289461282/374333754375\) \(558877300611840000\) \([2]\) \(1572864\) \(2.1688\)  
115920.s1 115920r4 \([0, 0, 0, -1199523, 505601602]\) \(127847420666360642/17899707105\) \(26724119510108160\) \([2]\) \(1572864\) \(2.1688\)  

Rank

sage: E.rank()
 

The elliptic curves in class 115920r have rank \(1\).

Complex multiplication

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

Modular form 115920.2.a.r

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