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Properties

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

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 92510f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92510.l2 92510f1 \([1, 0, 1, 8392, -1193882]\) \(109902239/1100000\) \(-654305653100000\) \([]\) \(490000\) \(1.5240\) \(\Gamma_0(N)\)-optimal
92510.l1 92510f2 \([1, 0, 1, -4995558, -4297997442]\) \(-23178622194826561/1610510\) \(-957968906703710\) \([]\) \(2450000\) \(2.3287\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 92510.2.a.f

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.