# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("8190.h1")

sage: E.isogeny_class()

## Elliptic curves in class 8190m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
8190.h7 8190m1 [1, -1, 0, -231525, -42591339] [2] 73728 $$\Gamma_0(N)$$-optimal
8190.h6 8190m2 [1, -1, 0, -372645, 15578325] [2, 2] 147456
8190.h5 8190m3 [1, -1, 0, -1430325, 630090981] [6] 221184
8190.h4 8190m4 [1, -1, 0, -4467645, 3629825325] [2] 294912
8190.h8 8190m5 [1, -1, 0, 1464435, 122496381] [2] 294912
8190.h2 8190m6 [1, -1, 0, -22607145, 41378528025] [2, 6] 442368
8190.h1 8190m7 [1, -1, 0, -361714095, 2647958009895] [6] 884736
8190.h3 8190m8 [1, -1, 0, -22329315, 42444895131] [6] 884736

## Rank

sage: E.rank()

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

## Modular form8190.2.a.h

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.