Properties

Label 20328.g
Number of curves $4$
Conductor $20328$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 20328.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
20328.g1 20328p3 \([0, -1, 0, -77468112, 186113921292]\) \(14171198121996897746/4077720290568771\) \(14794609122673259564095488\) \([2]\) \(5529600\) \(3.5361\)  
20328.g2 20328p2 \([0, -1, 0, -71026072, 230391350620]\) \(21843440425782779332/3100814593569\) \(5625120975050435798016\) \([2, 2]\) \(2764800\) \(3.1895\)  
20328.g3 20328p1 \([0, -1, 0, -71023652, 230407834692]\) \(87364831012240243408/1760913\) \(798608587569408\) \([4]\) \(1382400\) \(2.8429\) \(\Gamma_0(N)\)-optimal
20328.g4 20328p4 \([0, -1, 0, -64622752, 273613760620]\) \(-8226100326647904626/4152140742401883\) \(-15064618200576455166695424\) \([2]\) \(5529600\) \(3.5361\)  

Rank

sage: E.rank()
 

The elliptic curves in class 20328.g have rank \(1\).

Complex multiplication

The elliptic curves in class 20328.g do not have complex multiplication.

Modular form 20328.2.a.g

sage: E.q_eigenform(10)
 
\(q - q^{3} + 2q^{5} - q^{7} + q^{9} + 6q^{13} - 2q^{15} + 2q^{17} + 8q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.