Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("ce1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 115920.ce

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.ce1 115920cg1 \([0, 0, 0, -597483, -173265318]\) \(292583028222603/8456021875\) \(681737742604800000\) \([2]\) \(1658880\) \(2.1999\) \(\Gamma_0(N)\)-optimal
115920.ce2 115920cg2 \([0, 0, 0, 143397, -574674102]\) \(4044759171237/1771943359375\) \(-142856852040000000000\) \([2]\) \(3317760\) \(2.5465\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 115920.2.a.ce

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