# Properties

 Label 8400.co Number of curves 4 Conductor 8400 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("8400.co1")

sage: E.isogeny_class()

## Elliptic curves in class 8400.co

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
8400.co1 8400cg3 [0, 1, 0, -45008, 3659988]  24576
8400.co2 8400cg2 [0, 1, 0, -3008, 47988] [2, 2] 12288
8400.co3 8400cg1 [0, 1, 0, -1008, -12012]  6144 $$\Gamma_0(N)$$-optimal
8400.co4 8400cg4 [0, 1, 0, 6992, 307988]  24576

## Rank

sage: E.rank()

The elliptic curves in class 8400.co have rank $$0$$.

## Modular form8400.2.a.co

sage: E.q_eigenform(10)

$$q + q^{3} + q^{7} + q^{9} + 6q^{13} - 2q^{17} + 8q^{19} + O(q^{20})$$

## 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. 