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Properties

Label 92910bi
Number of curves $3$
Conductor $92910$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bi1")
 
E.isogeny_class()
 

Elliptic curves in class 92910bi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92910.bd2 92910bi1 \([1, 0, 0, -1577130, 794918052]\) \(-433836620224795849583521/22005928611000000000\) \(-22005928611000000000\) \([9]\) \(3394224\) \(2.4720\) \(\Gamma_0(N)\)-optimal
92910.bd3 92910bi2 \([1, 0, 0, 8277870, 1819757052]\) \(62730610483865150939136479/37731927035519394651000\) \(-37731927035519394651000\) \([3]\) \(10182672\) \(3.0213\)  
92910.bd1 92910bi3 \([1, 0, 0, -101809080, -441623441058]\) \(-116703330783653990330906728321/16713618975051084640111710\) \(-16713618975051084640111710\) \([]\) \(30548016\) \(3.5706\)  

Rank

sage: E.rank()
 

The elliptic curves in class 92910bi have rank \(0\).

Complex multiplication

The elliptic curves in class 92910bi do not have complex multiplication.

Modular form 92910.2.a.bi

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

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.