# Properties

 Label 100800fr Number of curves 8 Conductor 100800 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("100800.iy1")

sage: E.isogeny_class()

## Elliptic curves in class 100800fr

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
100800.iy7 100800fr1 [0, 0, 0, 3023700, -1524962000] [2] 4718592 $$\Gamma_0(N)$$-optimal
100800.iy6 100800fr2 [0, 0, 0, -15408300, -13653218000] [2, 2] 9437184
100800.iy5 100800fr3 [0, 0, 0, -108720300, 426592798000] [2, 2] 18874368
100800.iy4 100800fr4 [0, 0, 0, -217008300, -1230107618000] [2] 18874368
100800.iy8 100800fr5 [0, 0, 0, 18287700, 1363657822000] [2] 37748736
100800.iy2 100800fr6 [0, 0, 0, -1728720300, 27665272798000] [2, 2] 37748736
100800.iy3 100800fr7 [0, 0, 0, -1717920300, 28028001598000] [2] 75497472
100800.iy1 100800fr8 [0, 0, 0, -27659520300, 1770578063998000] [2] 75497472

## Rank

sage: E.rank()

The elliptic curves in class 100800fr have rank $$1$$.

## Modular form 100800.2.a.iy

sage: E.q_eigenform(10)

$$q + q^{7} - 4q^{11} - 2q^{13} + 2q^{17} - 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 4 & 8 & 8 & 16 & 16 \\ 2 & 1 & 2 & 2 & 4 & 4 & 8 & 8 \\ 4 & 2 & 1 & 4 & 2 & 2 & 4 & 4 \\ 4 & 2 & 4 & 1 & 8 & 8 & 16 & 16 \\ 8 & 4 & 2 & 8 & 1 & 4 & 8 & 8 \\ 8 & 4 & 2 & 8 & 4 & 1 & 2 & 2 \\ 16 & 8 & 4 & 16 & 8 & 2 & 1 & 4 \\ 16 & 8 & 4 & 16 & 8 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.