# Properties

 Label 100800ed Number of curves 4 Conductor 100800 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("100800.w1")

sage: E.isogeny_class()

## Elliptic curves in class 100800ed

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
100800.w4 100800ed1 [0, 0, 0, -661575, 862373500] [2] 2949120 $$\Gamma_0(N)$$-optimal
100800.w3 100800ed2 [0, 0, 0, -18239700, 29901436000] [2, 2] 5898240
100800.w2 100800ed3 [0, 0, 0, -26114700, 1567186000] [2] 11796480
100800.w1 100800ed4 [0, 0, 0, -291614700, 1916735686000] [2] 11796480

## Rank

sage: E.rank()

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

## Modular form 100800.2.a.w

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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.