# Properties

 Label 100800.ef Number of curves $4$ Conductor $100800$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("100800.ef1")

sage: E.isogeny_class()

## Elliptic curves in class 100800.ef

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
100800.ef1 100800c3 [0, 0, 0, -1514700, -716634000] [2] 1327104
100800.ef2 100800c4 [0, 0, 0, -1082700, -1133946000] [2] 2654208
100800.ef3 100800c1 [0, 0, 0, -74700, 6886000] [2] 442368 $$\Gamma_0(N)$$-optimal
100800.ef4 100800c2 [0, 0, 0, 117300, 36454000] [2] 884736

## Rank

sage: E.rank()

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

## Modular form 100800.2.a.ef

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 LMFDB 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 LMFDB labels.