# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("100800.a1")

sage: E.isogeny_class()

## Elliptic curves in class 100800hj

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
100800.a2 100800hj1 [0, 0, 0, -6375, -362500]  327680 $$\Gamma_0(N)$$-optimal
100800.a1 100800hj2 [0, 0, 0, -124500, -16900000]  655360

## Rank

sage: E.rank()

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

## Modular form 100800.2.a.a

sage: E.q_eigenform(10)

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

## 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. 