Properties

Label 115920.ca
Number of curves $2$
Conductor $115920$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("ca1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 115920.ca

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.ca1 115920di1 \([0, 0, 0, -17191803, 27435410602]\) \(188191720927962271801/9422571110400\) \(28135646574516633600\) \([2]\) \(5308416\) \(2.8029\) \(\Gamma_0(N)\)-optimal
115920.ca2 115920di2 \([0, 0, 0, -16270203, 30507472042]\) \(-159520003524722950201/42335913815758080\) \(-126414361279232574750720\) \([2]\) \(10616832\) \(3.1494\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 115920.2.a.ca

sage: E.q_eigenform(10)
 
\(q - q^{5} + q^{7} + 2 q^{11} + 4 q^{13} - 6 q^{17} + 4 q^{19} + O(q^{20})\)  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 LMFDB 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 LMFDB labels.