# Properties

 Label 100800cy Number of curves 8 Conductor 100800 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("100800.ea1")

sage: E.isogeny_class()

## Elliptic curves in class 100800cy

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
100800.ea7 100800cy1 [0, 0, 0, -7164300, -7378058000] [2] 3538944 $$\Gamma_0(N)$$-optimal
100800.ea6 100800cy2 [0, 0, 0, -8316300, -4845962000] [2, 2] 7077888
100800.ea5 100800cy3 [0, 0, 0, -21204300, 28562182000] [2] 10616832
100800.ea8 100800cy4 [0, 0, 0, 27683700, -35589962000] [2] 14155776
100800.ea4 100800cy5 [0, 0, 0, -62748300, 187952182000] [2] 14155776
100800.ea2 100800cy6 [0, 0, 0, -316116300, 2163135238000] [2, 2] 21233664
100800.ea3 100800cy7 [0, 0, 0, -293076300, 2491823878000] [2] 42467328
100800.ea1 100800cy8 [0, 0, 0, -5057748300, 138447122182000] [2] 42467328

## Rank

sage: E.rank()

The elliptic curves in class 100800cy have rank $$0$$.

## Modular form 100800.2.a.ea

sage: E.q_eigenform(10)

$$q - q^{7} + 2q^{13} - 6q^{17} - 8q^{19} + O(q^{20})$$

## 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.