# Properties

 Label 100800.df Number of curves 4 Conductor 100800 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("100800.df1")

sage: E.isogeny_class()

## Elliptic curves in class 100800.df

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
100800.df1 100800dc4 [0, 0, 0, -1620300, 793798000]  1572864
100800.df2 100800dc2 [0, 0, 0, -108300, 10582000] [2, 2] 786432
100800.df3 100800dc1 [0, 0, 0, -36300, -2522000]  393216 $$\Gamma_0(N)$$-optimal
100800.df4 100800dc3 [0, 0, 0, 251700, 66022000]  1572864

## Rank

sage: E.rank()

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

## Modular form 100800.2.a.df

sage: E.q_eigenform(10)

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

## 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 LMFDB 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 LMFDB labels. 