Properties

Label 91035.i
Number of curves $2$
Conductor $91035$
CM no
Rank $2$
Graph

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 91035.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
91035.i1 91035l2 \([1, -1, 1, -36698, 2715036]\) \(1526038582697/2205\) \(7897377285\) \([2]\) \(131072\) \(1.1698\)  
91035.i2 91035l1 \([1, -1, 1, -2273, 43656]\) \(-362467097/14175\) \(-50768853975\) \([2]\) \(65536\) \(0.82324\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 91035.i have rank \(2\).

Complex multiplication

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

Modular form 91035.2.a.i

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{4} - q^{5} - q^{7} + 3 q^{8} + q^{10} - 2 q^{11} - 4 q^{13} + q^{14} - q^{16} + O(q^{20})\) 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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.