Properties

Label 143570.t
Number of curves 2
Conductor 143570
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("143570.t1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 143570.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
143570.t1 143570j2 [1, -1, 1, -271752123, 1725371401177] [] 132765696  
143570.t2 143570j1 [1, -1, 1, 469827, -801227003] [] 18966528 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 143570.t have rank \(0\).

Modular form 143570.2.a.t

sage: E.q_eigenform(10)
 
\( q + q^{2} + 3q^{3} + q^{4} - q^{5} + 3q^{6} + q^{8} + 6q^{9} - q^{10} + 5q^{11} + 3q^{12} - 7q^{13} - 3q^{15} + q^{16} + 3q^{17} + 6q^{18} + 8q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.