↑

Properties

Label 2366.e
Number of curves $3$
Conductor $2366$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 2366.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2366.e1 2366a3 \([1, 0, 1, -2647051, -1657865324]\) \(-424962187484640625/182\) \(-878479238\) \([]\) \(18144\) \(1.9629\)  
2366.e2 2366a2 \([1, 0, 1, -32621, -2285216]\) \(-795309684625/6028568\) \(-29098746279512\) \([]\) \(6048\) \(1.4136\)  
2366.e3 2366a1 \([1, 0, 1, 1179, -16560]\) \(37595375/46592\) \(-224890684928\) \([]\) \(2016\) \(0.86432\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 2366.e have rank \(1\).

Complex multiplication

The elliptic curves in class 2366.e do not have complex multiplication.

Modular form 2366.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} - q^{7} - q^{8} - 2 q^{9} + 3 q^{11} + q^{12} + q^{14} + q^{16} + 2 q^{18} - 2 q^{19} + O(q^{20})\) Copy content 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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.