# Properties

 Label 100800.lm Number of curves 4 Conductor 100800 CM no Rank 2 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("100800.lm1")

sage: E.isogeny_class()

## Elliptic curves in class 100800.lm

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
100800.lm1 100800nb4 [0, 0, 0, -1620300, -793798000] [2] 1572864
100800.lm2 100800nb2 [0, 0, 0, -108300, -10582000] [2, 2] 786432
100800.lm3 100800nb1 [0, 0, 0, -36300, 2522000] [2] 393216 $$\Gamma_0(N)$$-optimal
100800.lm4 100800nb3 [0, 0, 0, 251700, -66022000] [2] 1572864

## Rank

sage: E.rank()

The elliptic curves in class 100800.lm have rank $$2$$.

## Modular form 100800.2.a.lm

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.