# Properties

 Label 8190bv Number of curves 8 Conductor 8190 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("8190.bx1")

sage: E.isogeny_class()

## Elliptic curves in class 8190bv

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
8190.bx7 8190bv1 [1, -1, 1, -30812, -3066721] [2] 55296 $$\Gamma_0(N)$$-optimal
8190.bx6 8190bv2 [1, -1, 1, -555692, -159271009] [2, 2] 110592
8190.bx8 8190bv3 [1, -1, 1, 249853, 45738371] [6] 165888
8190.bx3 8190bv4 [1, -1, 1, -8890592, -10201158529] [2] 221184
8190.bx5 8190bv5 [1, -1, 1, -618872, -120756481] [4] 221184
8190.bx4 8190bv6 [1, -1, 1, -1409027, 429934979] [2, 6] 331776
8190.bx2 8190bv7 [1, -1, 1, -8969027, -10011937021] [6] 663552
8190.bx1 8190bv8 [1, -1, 1, -20391107, 35440483331] [12] 663552

## Rank

sage: E.rank()

The elliptic curves in class 8190bv have rank $$0$$.

## Modular form8190.2.a.bx

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + q^{5} + q^{7} + q^{8} + q^{10} + q^{13} + q^{14} + q^{16} + 6q^{17} - 4q^{19} + O(q^{20})$$

## 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 Cremona numbering.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.