Properties

Label 102c
Number of curves 4
Conductor 102
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("102.b1")
sage: E.isogeny_class()

Elliptic curves in class 102c

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
102.b2 102c1 [1, 0, 1, -256, 1550] 6 24 \(\Gamma_0(N)\)-optimal
102.b3 102c2 [1, 0, 1, -216, 2062] 6 48  
102.b1 102c3 [1, 0, 1, -751, -6046] 2 72  
102.b4 102c4 [1, 0, 1, 1809, -37790] 2 144  

Rank

sage: E.rank()

The elliptic curves in class 102c have rank \(0\).

Modular form 102.2.a.b

sage: E.q_eigenform(10)
\( q - q^{2} + q^{3} + q^{4} - q^{6} + 2q^{7} - q^{8} + q^{9} + q^{12} + 2q^{13} - 2q^{14} + q^{16} - q^{17} - q^{18} - 4q^{19} + O(q^{20}) \)

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 Cremona 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 Cremona labels.