# Properties

 Label 88200gu Number of curves $6$ Conductor $88200$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("88200.hg1")

sage: E.isogeny_class()

## Elliptic curves in class 88200gu

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
88200.hg4 88200gu1 [0, 0, 0, -1933050, 1034445125] [2] 1179648 $$\Gamma_0(N)$$-optimal
88200.hg3 88200gu2 [0, 0, 0, -1988175, 972319250] [2, 2] 2359296
88200.hg5 88200gu3 [0, 0, 0, 2642325, 4829525750] [2] 4718592
88200.hg2 88200gu4 [0, 0, 0, -7500675, -6860943250] [2, 2] 4718592
88200.hg6 88200gu5 [0, 0, 0, 12344325, -37005498250] [2] 9437184
88200.hg1 88200gu6 [0, 0, 0, -115545675, -478045188250] [2] 9437184

## Rank

sage: E.rank()

The elliptic curves in class 88200gu have rank $$0$$.

## Modular form 88200.2.a.hg

sage: E.q_eigenform(10)

$$q + 4q^{11} - 2q^{13} - 2q^{17} + 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.