# Properties

 Label 62790w Number of curves 8 Conductor 62790 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("62790.v1")

sage: E.isogeny_class()

## Elliptic curves in class 62790w

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
62790.v7 62790w1 [1, 0, 1, -134368, 149877806] [6] 1658880 $$\Gamma_0(N)$$-optimal
62790.v6 62790w2 [1, 0, 1, -5134368, 4453877806] [2, 6] 3317760
62790.v8 62790w3 [1, 0, 1, 1206257, -3990069694] [2] 4976640
62790.v5 62790w4 [1, 0, 1, -8239368, -1567338194] [6] 6635520
62790.v3 62790w5 [1, 0, 1, -82029368, 285951093806] [6] 6635520
62790.v4 62790w6 [1, 0, 1, -31561743, -65240015294] [2, 2] 9953280
62790.v1 62790w7 [1, 0, 1, -498774543, -4287535531454] [2] 19906560
62790.v2 62790w8 [1, 0, 1, -88636943, 237190054466] [2] 19906560

## Rank

sage: E.rank()

The elliptic curves in class 62790w have rank $$1$$.

## Modular form 62790.2.a.v

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} + q^{7} - q^{8} + q^{9} - q^{10} + q^{12} + q^{13} - q^{14} + q^{15} + q^{16} + 6q^{17} - q^{18} - 4q^{19} + O(q^{20})$$

## 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 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.