Properties

Label 90.c
Number of curves 8
Conductor 90
CM no
Rank 0
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath

sage: E = EllipticCurve("90.c1")
sage: E.isogeny_class()

Elliptic curves in class 90.c

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
90.c1 90c8 [1, -1, 1, -48002, 4059929] 6 192  
90.c2 90c7 [1, -1, 1, -4082, 14681] 6 192  
90.c3 90c6 [1, -1, 1, -3002, 63929] 12 96  
90.c4 90c4 [1, -1, 1, -2597, -50281] 2 64  
90.c5 90c5 [1, -1, 1, -617, 5231] 2 64  
90.c6 90c2 [1, -1, 1, -167, -709] 4 32  
90.c7 90c3 [1, -1, 1, -122, 1721] 12 48  
90.c8 90c1 [1, -1, 1, 13, -61] 4 16 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curves in class 90.c have rank \(0\).

Modular form 90.2.a.c

sage: E.q_eigenform(10)
\( q + q^{2} + q^{4} + q^{5} - 4q^{7} + q^{8} + q^{10} + 2q^{13} - 4q^{14} + q^{16} - 6q^{17} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 4 & 2 & 12 & 3 & 6 & 4 & 12 \\ 4 & 1 & 2 & 3 & 12 & 6 & 4 & 12 \\ 2 & 2 & 1 & 6 & 6 & 3 & 2 & 6 \\ 12 & 3 & 6 & 1 & 4 & 2 & 12 & 4 \\ 3 & 12 & 6 & 4 & 1 & 2 & 12 & 4 \\ 6 & 6 & 3 & 2 & 2 & 1 & 6 & 2 \\ 4 & 4 & 2 & 12 & 12 & 6 & 1 & 3 \\ 12 & 12 & 6 & 4 & 4 & 2 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.