Properties

Label 115520.r
Number of curves $2$
Conductor $115520$
CM no
Rank $1$
Graph

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

Elliptic curves in class 115520.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115520.r1 115520cn2 \([0, 1, 0, -420685, 78062025]\) \(7575076864/1953125\) \(2122945380125000000\) \([]\) \(2068416\) \(2.2259\)  
115520.r2 115520cn1 \([0, 1, 0, -146325, -21585527]\) \(318767104/125\) \(135868504328000\) \([]\) \(689472\) \(1.6766\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 115520.r have rank \(1\).

Complex multiplication

The elliptic curves in class 115520.r do not have complex multiplication.

Modular form 115520.2.a.r

sage: E.q_eigenform(10)
 
\(q - 2 q^{3} + q^{5} + 4 q^{7} + q^{9} + 3 q^{11} - 2 q^{13} - 2 q^{15} + 6 q^{17} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.