# Properties

 Label 100800jo Number of curves $4$ Conductor $100800$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("100800.ml1")

sage: E.isogeny_class()

## Elliptic curves in class 100800jo

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
100800.ml2 100800jo1 [0, 0, 0, -168300, -26542000]  442368 $$\Gamma_0(N)$$-optimal
100800.ml3 100800jo2 [0, 0, 0, -120300, -41998000]  884736
100800.ml1 100800jo3 [0, 0, 0, -672300, 185922000]  1327104
100800.ml4 100800jo4 [0, 0, 0, 1055700, 984258000]  2654208

## Rank

sage: E.rank()

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

## Modular form 100800.2.a.ml

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 