Properties

Label 91035.q
Number of curves 4
Conductor 91035
CM no
Rank 1
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath

sage: E = EllipticCurve("91035.q1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 91035.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
91035.q1 91035bi4 [1, -1, 1, -292667, 61009566] [2] 655360  
91035.q2 91035bi2 [1, -1, 1, -19562, 817224] [2, 2] 327680  
91035.q3 91035bi1 [1, -1, 1, -6557, -191964] [2] 163840 \(\Gamma_0(N)\)-optimal
91035.q4 91035bi3 [1, -1, 1, 45463, 5056854] [2] 655360  

Rank

sage: E.rank()
 

The elliptic curves in class 91035.q have rank \(1\).

Modular form 91035.2.a.q

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

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.