Properties

Label 45177.c
Number of curves 4
Conductor 45177
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("45177.c1")
sage: E.isogeny_class()

Elliptic curves in class 45177.c

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
45177.c1 45177a4 [1, 1, 1, -200587, 34460654] 2 304128  
45177.c2 45177a2 [1, 1, 1, -15772, 232916] 4 152064  
45177.c3 45177a1 [1, 1, 1, -8927, -325636] 2 76032 \(\Gamma_0(N)\)-optimal
45177.c4 45177a3 [1, 1, 1, 59523, 1889406] 2 304128  

Rank

sage: E.rank()

The elliptic curves in class 45177.c have rank \(0\).

Modular form 45177.2.a.c

sage: E.q_eigenform(10)
\( q - q^{2} - q^{3} - q^{4} + 2q^{5} + q^{6} + 4q^{7} + 3q^{8} + q^{9} - 2q^{10} + q^{11} + q^{12} + 2q^{13} - 4q^{14} - 2q^{15} - q^{16} + 2q^{17} - q^{18} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.