# Properties

 Label 8400bk Number of curves $4$ Conductor $8400$ CM no Rank $0$ Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("bk1")

sage: E.isogeny_class()

## Elliptic curves in class 8400bk

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
8400.m3 8400bk1 [0, -1, 0, -1408, 13312] [2] 9216 $$\Gamma_0(N)$$-optimal
8400.m2 8400bk2 [0, -1, 0, -9408, -338688] [2, 2] 18432
8400.m1 8400bk3 [0, -1, 0, -149408, -22178688] [2] 36864
8400.m4 8400bk4 [0, -1, 0, 2592, -1154688] [2] 36864

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 8400bk do not have complex multiplication.

## Modular form8400.2.a.bk

sage: E.q_eigenform(10)

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

## 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.