Properties

Label 236691.l
Number of curves $3$
Conductor $236691$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 236691.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
236691.l1 236691l3 \([0, 0, 1, -305184, 159934117]\) \(-178643795968/524596891\) \(-9230957873545826691\) \([]\) \(3981312\) \(2.3260\)  
236691.l2 236691l1 \([0, 0, 1, -19074, -1015763]\) \(-43614208/91\) \(-1601262189891\) \([]\) \(442368\) \(1.2274\) \(\Gamma_0(N)\)-optimal
236691.l3 236691l2 \([0, 0, 1, 32946, -5039510]\) \(224755712/753571\) \(-13260052194487371\) \([]\) \(1327104\) \(1.7767\)  

Rank

sage: E.rank()
 

The elliptic curves in class 236691.l have rank \(1\).

Complex multiplication

The elliptic curves in class 236691.l do not have complex multiplication.

Modular form 236691.2.a.l

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

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.