Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("q1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 91035.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
91035.q1 91035bi4 \([1, -1, 1, -292667, 61009566]\) \(157551496201/13125\) \(230951277388125\) \([2]\) \(655360\) \(1.8000\)  
91035.q2 91035bi2 \([1, -1, 1, -19562, 817224]\) \(47045881/11025\) \(193999073006025\) \([2, 2]\) \(327680\) \(1.4534\)  
91035.q3 91035bi1 \([1, -1, 1, -6557, -191964]\) \(1771561/105\) \(1847610219105\) \([2]\) \(163840\) \(1.1068\) \(\Gamma_0(N)\)-optimal
91035.q4 91035bi3 \([1, -1, 1, 45463, 5056854]\) \(590589719/972405\) \(-17110718239131405\) \([2]\) \(655360\) \(1.8000\)  

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 91035.q do not have complex multiplication.

Modular form 91035.2.a.q

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.