Properties

Label 20097.l
Number of curves $4$
Conductor $20097$
CM no
Rank $1$
Graph

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

Elliptic curves in class 20097.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
20097.l1 20097h3 \([1, -1, 0, -480201, -127946386]\) \(16798320881842096017/2132227789307\) \(1554394058404803\) \([2]\) \(172032\) \(1.9368\)  
20097.l2 20097h4 \([1, -1, 0, -190491, 30741092]\) \(1048626554636928177/48569076788309\) \(35406856978677261\) \([2]\) \(172032\) \(1.9368\)  
20097.l3 20097h2 \([1, -1, 0, -32586, -1629433]\) \(5249244962308257/1448621666569\) \(1056045194928801\) \([2, 2]\) \(86016\) \(1.5903\)  
20097.l4 20097h1 \([1, -1, 0, 5259, -168616]\) \(22062729659823/29354283343\) \(-21399272557047\) \([2]\) \(43008\) \(1.2437\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 20097.l have rank \(1\).

Complex multiplication

The elliptic curves in class 20097.l do not have complex multiplication.

Modular form 20097.2.a.l

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.