# Properties

 Label 100800.mj Number of curves 8 Conductor 100800 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("100800.mj1")

sage: E.isogeny_class()

## Elliptic curves in class 100800.mj

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
100800.mj1 100800mw8 [0, 0, 0, -5057748300, -138447122182000] [2] 42467328
100800.mj2 100800mw6 [0, 0, 0, -316116300, -2163135238000] [2, 2] 21233664
100800.mj3 100800mw7 [0, 0, 0, -293076300, -2491823878000] [2] 42467328
100800.mj4 100800mw5 [0, 0, 0, -62748300, -187952182000] [2] 14155776
100800.mj5 100800mw3 [0, 0, 0, -21204300, -28562182000] [2] 10616832
100800.mj6 100800mw2 [0, 0, 0, -8316300, 4845962000] [2, 2] 7077888
100800.mj7 100800mw1 [0, 0, 0, -7164300, 7378058000] [2] 3538944 $$\Gamma_0(N)$$-optimal
100800.mj8 100800mw4 [0, 0, 0, 27683700, 35589962000] [2] 14155776

## Rank

sage: E.rank()

The elliptic curves in class 100800.mj have rank $$0$$.

## Modular form 100800.2.a.mj

sage: E.q_eigenform(10)

$$q + q^{7} + 2q^{13} - 6q^{17} + 8q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 3 & 4 & 6 & 12 & 12 \\ 2 & 1 & 2 & 6 & 2 & 3 & 6 & 6 \\ 4 & 2 & 1 & 12 & 4 & 6 & 12 & 3 \\ 3 & 6 & 12 & 1 & 12 & 2 & 4 & 4 \\ 4 & 2 & 4 & 12 & 1 & 6 & 3 & 12 \\ 6 & 3 & 6 & 2 & 6 & 1 & 2 & 2 \\ 12 & 6 & 12 & 4 & 3 & 2 & 1 & 4 \\ 12 & 6 & 3 & 4 & 12 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.