# Properties

 Label 100800hi Number of curves 2 Conductor 100800 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("100800.e1")

sage: E.isogeny_class()

## Elliptic curves in class 100800hi

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
100800.e1 100800hi1 [0, 0, 0, -10380, -394000]  196608 $$\Gamma_0(N)$$-optimal
100800.e2 100800hi2 [0, 0, 0, 4020, -1402000]  393216

## Rank

sage: E.rank()

The elliptic curves in class 100800hi have rank $$1$$.

## Modular form 100800.2.a.e

sage: E.q_eigenform(10)

$$q - q^{7} - 6q^{11} + 2q^{13} - 4q^{17} + 6q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 