Properties

Label 91091d
Number of curves $2$
Conductor $91091$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 91091d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
91091.d2 91091d1 \([1, 0, 0, 28811, -7139952]\) \(4657463/41503\) \(-23568277567457623\) \([2]\) \(622080\) \(1.8228\) \(\Gamma_0(N)\)-optimal
91091.d1 91091d2 \([1, 0, 0, -426644, -99050771]\) \(15124197817/1294139\) \(734901745967087699\) \([2]\) \(1244160\) \(2.1694\)  

Rank

sage: E.rank()
 

The elliptic curves in class 91091d have rank \(0\).

Complex multiplication

The elliptic curves in class 91091d do not have complex multiplication.

Modular form 91091.2.a.d

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.