Properties

 Label 102.c Number of curves 6 Conductor 102 CM no Rank 0 Graph Related objects

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 form102.2.a.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()

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels. 