# Properties

 Label 100800.ja Number of curves $6$ Conductor $100800$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("100800.ja1")

sage: E.isogeny_class()

## Elliptic curves in class 100800.ja

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
100800.ja1 100800fq6 [0, 0, 0, -9432300, 11149742000] [2] 3145728
100800.ja2 100800fq4 [0, 0, 0, -612300, 160022000] [2, 2] 1572864
100800.ja3 100800fq2 [0, 0, 0, -162300, -22678000] [2, 2] 786432
100800.ja4 100800fq1 [0, 0, 0, -157800, -24127000] [2] 393216 $$\Gamma_0(N)$$-optimal
100800.ja5 100800fq3 [0, 0, 0, 215700, -112642000] [2] 1572864
100800.ja6 100800fq5 [0, 0, 0, 1007700, 863102000] [2] 3145728

## Rank

sage: E.rank()

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

## Modular form 100800.2.a.ja

sage: E.q_eigenform(10)

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

## 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 LMFDB numbering.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 8 & 4 \\ 2 & 1 & 2 & 4 & 4 & 2 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 2 & 4 & 8 & 8 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.