# Properties

 Label 100800md Number of curves 4 Conductor 100800 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("100800.u1")

sage: E.isogeny_class()

## Elliptic curves in class 100800md

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
100800.u3 100800md1 [0, 0, 0, -284700, -58466000] [2] 589824 $$\Gamma_0(N)$$-optimal
100800.u2 100800md2 [0, 0, 0, -302700, -50654000] [2, 2] 1179648
100800.u4 100800md3 [0, 0, 0, 669300, -309206000] [2] 2359296
100800.u1 100800md4 [0, 0, 0, -1562700, 707866000] [2] 2359296

## Rank

sage: E.rank()

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

## Modular form 100800.2.a.u

sage: E.q_eigenform(10)

$$q - q^{7} - 4q^{11} - 2q^{13} - 6q^{17} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.