Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("cc1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 115920.cc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.cc1 115920g2 \([0, 0, 0, -310203, 66480202]\) \(59699126465470854/19845765625\) \(1097391456000000\) \([2]\) \(638976\) \(1.8589\)  
115920.cc2 115920g1 \([0, 0, 0, -22083, 731218]\) \(43075884983148/16573802875\) \(458232501888000\) \([2]\) \(319488\) \(1.5123\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 115920.2.a.cc

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