Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("ct1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 115920ct

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.r2 115920ct1 \([0, 0, 0, -232203, 43066298]\) \(463702796512201/15214500\) \(45430253568000\) \([2]\) \(552960\) \(1.7143\) \(\Gamma_0(N)\)-optimal
115920.r3 115920ct2 \([0, 0, 0, -222123, 46975322]\) \(-405897921250921/84358968750\) \(-251894530944000000\) \([2]\) \(1105920\) \(2.0609\)  
115920.r1 115920ct3 \([0, 0, 0, -415803, -33939862]\) \(2662558086295801/1374177967680\) \(4103273424644997120\) \([2]\) \(1658880\) \(2.2636\)  
115920.r4 115920ct4 \([0, 0, 0, 1559877, -263513878]\) \(140574743422291079/91397357868600\) \(-272911048237913702400\) \([2]\) \(3317760\) \(2.6102\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 115920.2.a.ct

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

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.