Properties

Label 2318.d
Number of curves $2$
Conductor $2318$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 2318.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2318.d1 2318e2 \([1, 1, 1, -82015, -9074589]\) \(-61010405398305333361/32094659438\) \(-32094659438\) \([]\) \(8300\) \(1.3466\)  
2318.d2 2318e1 \([1, 1, 1, 255, -2849]\) \(1833318007919/4833345248\) \(-4833345248\) \([5]\) \(1660\) \(0.54192\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 2318.d have rank \(0\).

Complex multiplication

The elliptic curves in class 2318.d do not have complex multiplication.

Modular form 2318.2.a.d

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - 4 q^{5} - q^{6} - 2 q^{7} + q^{8} - 2 q^{9} - 4 q^{10} - 3 q^{11} - q^{12} - q^{13} - 2 q^{14} + 4 q^{15} + q^{16} - 2 q^{17} - 2 q^{18} + q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.