Properties

Label 182585.e
Number of curves $2$
Conductor $182585$
CM no
Rank $0$
Graph

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

Elliptic curves in class 182585.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
182585.e1 182585d1 \([1, 1, 0, -2867, 11384]\) \(117649/65\) \(1440683473385\) \([2]\) \(302848\) \(1.0235\) \(\Gamma_0(N)\)-optimal
182585.e2 182585d2 \([1, 1, 0, 11178, 104081]\) \(6967871/4225\) \(-93644425770025\) \([2]\) \(605696\) \(1.3701\)  

Rank

sage: E.rank()
 

The elliptic curves in class 182585.e have rank \(0\).

Complex multiplication

The elliptic curves in class 182585.e do not have complex multiplication.

Modular form 182585.2.a.e

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

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.