Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 115920.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.i1 115920cw2 \([0, 0, 0, -106203, -23798]\) \(44365623586201/25674468750\) \(76663552896000000\) \([2]\) \(884736\) \(1.9293\)  
115920.i2 115920cw1 \([0, 0, 0, -73083, -7581782]\) \(14457238157881/49990500\) \(149270833152000\) \([2]\) \(442368\) \(1.5827\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 115920.2.a.i

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