Properties

Label 28322t
Number of curves 4
Conductor 28322
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("28322.bb1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 28322t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
28322.bb3 28322t1 [1, -1, 1, -264634, -51489175] [2] 221184 \(\Gamma_0(N)\)-optimal
28322.bb2 28322t2 [1, -1, 1, -547854, 78338873] [2, 2] 442368  
28322.bb4 28322t3 [1, -1, 1, 1859516, 579071833] [2] 884736  
28322.bb1 28322t4 [1, -1, 1, -7486744, 7883202345] [2] 884736  

Rank

sage: E.rank()
 

The elliptic curves in class 28322t have rank \(1\).

Modular form 28322.2.a.bb

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{4} + 2q^{5} + q^{8} - 3q^{9} + 2q^{10} + 2q^{13} + q^{16} - 3q^{18} - 4q^{19} + O(q^{20}) \)

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 Cremona 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 Cremona labels.