Properties

Label 38640bd
Number of curves $4$
Conductor $38640$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bd1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 38640bd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
38640.g3 38640bd1 \([0, -1, 0, -2033976, -1195140240]\) \(-227196402372228188089/19338934824115200\) \(-79212277039575859200\) \([2]\) \(1105920\) \(2.5631\) \(\Gamma_0(N)\)-optimal
38640.g2 38640bd2 \([0, -1, 0, -33181496, -73557058704]\) \(986396822567235411402169/6336721794060000\) \(25955212468469760000\) \([2]\) \(2211840\) \(2.9096\)  
38640.g4 38640bd3 \([0, -1, 0, 12058584, -48234384]\) \(47342661265381757089751/27397579603968000000\) \(-112220486057852928000000\) \([2]\) \(3317760\) \(3.1124\)  
38640.g1 38640bd4 \([0, -1, 0, -48234536, -337641360]\) \(3029968325354577848895529/1753440696000000000000\) \(7182093090816000000000000\) \([2]\) \(6635520\) \(3.4589\)  

Rank

sage: E.rank()
 

The elliptic curves in class 38640bd have rank \(0\).

Complex multiplication

The elliptic curves in class 38640bd do not have complex multiplication.

Modular form 38640.2.a.bd

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} - q^{7} + q^{9} - 4q^{13} + q^{15} - 2q^{19} + O(q^{20})\)  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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.