# Properties

 Label 8400.k Number of curves $6$ Conductor $8400$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("8400.k1")

sage: E.isogeny_class()

## Elliptic curves in class 8400.k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
8400.k1 8400bl3 [0, -1, 0, -537608, -151542288] [2] 49152
8400.k2 8400bl5 [0, -1, 0, -365608, 84393712] [2] 98304
8400.k3 8400bl4 [0, -1, 0, -41608, -1142288] [2, 2] 49152
8400.k4 8400bl2 [0, -1, 0, -33608, -2358288] [2, 2] 24576
8400.k5 8400bl1 [0, -1, 0, -1608, -54288] [2] 12288 $$\Gamma_0(N)$$-optimal
8400.k6 8400bl6 [0, -1, 0, 154392, -8982288] [2] 98304

## Rank

sage: E.rank()

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

## Modular form8400.2.a.k

sage: E.q_eigenform(10)

$$q - q^{3} - q^{7} + q^{9} + 4q^{11} - 6q^{13} - 2q^{17} + 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.