Properties

Label 102.c
Number of curves 6
Conductor \(102\)
CM no
Rank \(0\)
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("102.c1")
sage: E.isogeny_class()

Elliptic curves in class 102.c

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
102.c1 102b5 [1, 0, 0, -27744, -1781010] 2 128  
102.c2 102b3 [1, 0, 0, -1734, -27936] 4 64  
102.c3 102b6 [1, 0, 0, -1644, -30942] 2 128  
102.c4 102b2 [1, 0, 0, -114, -396] 8 32  
102.c5 102b1 [1, 0, 0, -34, 68] 8 16 \(\Gamma_0(N)\)-optimal
102.c6 102b4 [1, 0, 0, 226, -2232] 4 64  

Rank

sage: E.rank()

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

Modular form 102.2.1.c

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

Isogeny matrix

sage: E.isogeny_class().matrix()

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

Isogeny graph

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