Properties

Label 115920cd
Number of curves $2$
Conductor $115920$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("cd1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 115920cd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.f1 115920cd1 \([0, 0, 0, -21843, 1059858]\) \(14295828483/2254000\) \(181721014272000\) \([2]\) \(331776\) \(1.4589\) \(\Gamma_0(N)\)-optimal
115920.f2 115920cd2 \([0, 0, 0, 38637, 5886162]\) \(79119341757/231437500\) \(-18658854144000000\) \([2]\) \(663552\) \(1.8055\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 115920.2.a.cd

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.