# Properties

 Label 100800nx Number of curves $6$ Conductor $100800$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("100800.iz1")

sage: E.isogeny_class()

## Elliptic curves in class 100800nx

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
100800.iz6 100800nx1 [0, 0, 0, 143700, -29342000] [2] 1179648 $$\Gamma_0(N)$$-optimal
100800.iz5 100800nx2 [0, 0, 0, -1008300, -303518000] [2, 2] 2359296
100800.iz4 100800nx3 [0, 0, 0, -5328300, 4474402000] [2] 4718592
100800.iz2 100800nx4 [0, 0, 0, -15120300, -22628702000] [2, 2] 4718592
100800.iz3 100800nx5 [0, 0, 0, -14112300, -25775678000] [2] 9437184
100800.iz1 100800nx6 [0, 0, 0, -241920300, -1448293502000] [2] 9437184

## Rank

sage: E.rank()

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

## Modular form 100800.2.a.iz

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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.