Properties

Label 259182.gd
Number of curves $2$
Conductor $259182$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("gd1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 259182.gd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
259182.gd1 259182gd1 \([1, -1, 1, -221, 1829]\) \(-13475473/7616\) \(-671799744\) \([]\) \(120960\) \(0.39693\) \(\Gamma_0(N)\)-optimal
259182.gd2 259182gd2 \([1, -1, 1, 1759, -24307]\) \(6827155247/6740636\) \(-594584760924\) \([]\) \(362880\) \(0.94624\)  

Rank

sage: E.rank()
 

The elliptic curves in class 259182.gd have rank \(0\).

Complex multiplication

The elliptic curves in class 259182.gd do not have complex multiplication.

Modular form 259182.2.a.gd

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.