# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("100800.o1")

sage: E.isogeny_class()

## Elliptic curves in class 100800hc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
100800.o2 100800hc1 [0, 0, 0, -110640, 23558600]  1032192 $$\Gamma_0(N)$$-optimal
100800.o1 100800hc2 [0, 0, 0, -2078940, 1153362800]  2064384

## Rank

sage: E.rank()

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

## Modular form 100800.2.a.o

sage: E.q_eigenform(10)

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

## 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. 