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Properties

Label 91358.d
Number of curves $2$
Conductor $91358$
CM no
Rank $1$
Graph

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

Elliptic curves in class 91358.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
91358.d1 91358e2 \([1, -1, 1, -2069779263, -36234533783817]\) \(980608845198487572940262772638529/275069582998987905611470576\) \(275069582998987905611470576\) \([]\) \(130658304\) \(4.0546\)  
91358.d2 91358e1 \([1, -1, 1, -62268303, 189138631383]\) \(26700832091472147512881229889/295971568928797229056\) \(295971568928797229056\) \([7]\) \(18665472\) \(3.0817\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 91358.d have rank \(1\).

Complex multiplication

The elliptic curves in class 91358.d do not have complex multiplication.

Modular form 91358.2.a.d

sage: E.q_eigenform(10)
 
\(q + q^{2} - 3 q^{3} + q^{4} - q^{5} - 3 q^{6} + q^{7} + q^{8} + 6 q^{9} - q^{10} - 2 q^{11} - 3 q^{12} - 7 q^{13} + q^{14} + 3 q^{15} + q^{16} + q^{17} + 6 q^{18} - 8 q^{19} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.