# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("100800.f1")

sage: E.isogeny_class()

## Elliptic curves in class 100800.f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
100800.f1 100800ej4 [0, 0, 0, -1645500, 812446000]  1327104
100800.f2 100800ej3 [0, 0, 0, -102000, 12913000]  663552
100800.f3 100800ej2 [0, 0, 0, -25500, 502000]  442368
100800.f4 100800ej1 [0, 0, 0, 6000, 61000]  221184 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form 100800.2.a.f

sage: E.q_eigenform(10)

$$q - q^{7} - 6q^{11} + 2q^{13} + 4q^{19} + O(q^{20})$$

## 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 LMFDB numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 