# Properties

 Label 2800.g Number of curves 6 Conductor 2800 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("2800.g1")

sage: E.isogeny_class()

## Elliptic curves in class 2800.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2800.g1 2800v6 [0, 1, 0, -1092208, 438981588] [2] 20736
2800.g2 2800v5 [0, 1, 0, -68208, 6853588] [2] 10368
2800.g3 2800v4 [0, 1, 0, -14208, 529588] [2] 6912
2800.g4 2800v2 [0, 1, 0, -4208, -106412] [2] 2304
2800.g5 2800v1 [0, 1, 0, -208, -2412] [2] 1152 $$\Gamma_0(N)$$-optimal
2800.g6 2800v3 [0, 1, 0, 1792, 49588] [2] 3456

## Rank

sage: E.rank()

The elliptic curves in class 2800.g have rank $$1$$.

## Modular form2800.2.a.g

sage: E.q_eigenform(10)

$$q - 2q^{3} + q^{7} + q^{9} + 4q^{13} - 6q^{17} - 2q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 9 & 18 & 6 \\ 2 & 1 & 6 & 18 & 9 & 3 \\ 3 & 6 & 1 & 3 & 6 & 2 \\ 9 & 18 & 3 & 1 & 2 & 6 \\ 18 & 9 & 6 & 2 & 1 & 3 \\ 6 & 3 & 2 & 6 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.