Properties

Label 195.a
Number of curves 8
Conductor 195
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("195.a1")
sage: E.isogeny_class()

Elliptic curves in class 195.a

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
195.a1 195a7 [1, 0, 0, -130000, -18051943] 2 384  
195.a2 195a5 [1, 0, 0, -8125, -282568] 4 192  
195.a3 195a8 [1, 0, 0, -7930, -296725] 2 384  
195.a4 195a3 [1, 0, 0, -520, -4225] 8 96  
195.a5 195a2 [1, 0, 0, -115, 392] 8 48  
195.a6 195a1 [1, 0, 0, -110, 435] 4 24 \(\Gamma_0(N)\)-optimal
195.a7 195a4 [1, 0, 0, 210, 2277] 4 96  
195.a8 195a6 [1, 0, 0, 605, -19750] 4 192  

Rank

sage: E.rank()

The elliptic curves in class 195.a have rank \(0\).

Modular form 195.2.a.a

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

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 LMFDB numbering.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 4 & 8 & 16 & 16 & 8 \\ 2 & 1 & 2 & 2 & 4 & 8 & 8 & 4 \\ 4 & 2 & 1 & 4 & 8 & 16 & 16 & 8 \\ 4 & 2 & 4 & 1 & 2 & 4 & 4 & 2 \\ 8 & 4 & 8 & 2 & 1 & 2 & 2 & 4 \\ 16 & 8 & 16 & 4 & 2 & 1 & 4 & 8 \\ 16 & 8 & 16 & 4 & 2 & 4 & 1 & 8 \\ 8 & 4 & 8 & 2 & 4 & 8 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.