Properties

Label 232562k
Number of curves $2$
Conductor $232562$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 232562k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
232562.k2 232562k1 \([1, 1, 1, 2863, -21185]\) \(24167/16\) \(-1718207126416\) \([]\) \(489600\) \(1.0365\) \(\Gamma_0(N)\)-optimal
232562.k1 232562k2 \([1, 1, 1, -49992, -4439863]\) \(-128667913/4096\) \(-439861024362496\) \([]\) \(1468800\) \(1.5858\)  

Rank

sage: E.rank()
 

The elliptic curves in class 232562k have rank \(0\).

Complex multiplication

The elliptic curves in class 232562k do not have complex multiplication.

Modular form 232562.2.a.k

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.