Properties

Label 92510n
Number of curves $2$
Conductor $92510$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("n1")
 
E.isogeny_class()
 

Elliptic curves in class 92510n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92510.p1 92510n1 \([1, 1, 1, -74446, 7861899]\) \(-76711450249/851840\) \(-506694297760640\) \([]\) \(698544\) \(1.6365\) \(\Gamma_0(N)\)-optimal
92510.p2 92510n2 \([1, 1, 1, 249339, 41017483]\) \(2882081488391/2883584000\) \(-1715223011262464000\) \([]\) \(2095632\) \(2.1858\)  

Rank

sage: E.rank()
 

The elliptic curves in class 92510n have rank \(0\).

Complex multiplication

The elliptic curves in class 92510n do not have complex multiplication.

Modular form 92510.2.a.n

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