# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("100800.mm1")

sage: E.isogeny_class()

## Elliptic curves in class 100800jn

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
100800.mm3 100800jn1 [0, 0, 0, -74700, -6886000]  442368 $$\Gamma_0(N)$$-optimal
100800.mm4 100800jn2 [0, 0, 0, 117300, -36454000]  884736
100800.mm1 100800jn3 [0, 0, 0, -1514700, 716634000]  1327104
100800.mm2 100800jn4 [0, 0, 0, -1082700, 1133946000]  2654208

## Rank

sage: E.rank()

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

## Modular form 100800.2.a.mm

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. 