Properties

Label 45968.t
Number of curves 4
Conductor 45968
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("45968.t1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 45968.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
45968.t1 45968k4 [0, -1, 0, -305608, 45037680] [2] 663552  
45968.t2 45968k3 [0, -1, 0, -278568, 56675696] [2] 331776  
45968.t3 45968k2 [0, -1, 0, -116328, -15229072] [2] 221184  
45968.t4 45968k1 [0, -1, 0, -8168, -173200] [2] 110592 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 45968.t have rank \(0\).

Modular form 45968.2.a.t

sage: E.q_eigenform(10)
 
\( q + 2q^{3} - 4q^{7} + q^{9} + 6q^{11} - q^{17} - 4q^{19} + O(q^{20}) \)

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.