Properties

Label 9900.bd
Number of curves 4
Conductor 9900
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("9900.bd1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 9900.bd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
9900.bd1 9900t4 [0, 0, 0, -1597575, 777212750] [2] 124416  
9900.bd2 9900t3 [0, 0, 0, -100200, 12054125] [2] 62208  
9900.bd3 9900t2 [0, 0, 0, -22575, 737750] [2] 41472  
9900.bd4 9900t1 [0, 0, 0, -10200, -388375] [2] 20736 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 9900.bd have rank \(0\).

Modular form 9900.2.a.bd

sage: E.q_eigenform(10)
 
\( q + 4q^{7} + q^{11} + 4q^{13} - 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.