# Properties

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

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 2800.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2800.g1 2800v6 $$[0, 1, 0, -1092208, 438981588]$$ $$2251439055699625/25088$$ $$1605632000000$$ $$[2]$$ $$20736$$ $$1.9110$$
2800.g2 2800v5 $$[0, 1, 0, -68208, 6853588]$$ $$-548347731625/1835008$$ $$-117440512000000$$ $$[2]$$ $$10368$$ $$1.5644$$
2800.g3 2800v4 $$[0, 1, 0, -14208, 529588]$$ $$4956477625/941192$$ $$60236288000000$$ $$[2]$$ $$6912$$ $$1.3617$$
2800.g4 2800v2 $$[0, 1, 0, -4208, -106412]$$ $$128787625/98$$ $$6272000000$$ $$[2]$$ $$2304$$ $$0.81236$$
2800.g5 2800v1 $$[0, 1, 0, -208, -2412]$$ $$-15625/28$$ $$-1792000000$$ $$[2]$$ $$1152$$ $$0.46578$$ $$\Gamma_0(N)$$-optimal
2800.g6 2800v3 $$[0, 1, 0, 1792, 49588]$$ $$9938375/21952$$ $$-1404928000000$$ $$[2]$$ $$3456$$ $$1.0151$$

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 2800.g do not have complex multiplication.

## Modular form2800.2.a.g

sage: E.q_eigenform(10)

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

## 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.