# Properties

 Label 23400bk Number of curves $4$ Conductor $23400$ CM no Rank $1$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 23400bk

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
23400.c4 23400bk1 $$[0, 0, 0, -4575, -422750]$$ $$-3631696/24375$$ $$-71077500000000$$ $$[2]$$ $$73728$$ $$1.3413$$ $$\Gamma_0(N)$$-optimal
23400.c3 23400bk2 $$[0, 0, 0, -117075, -15385250]$$ $$15214885924/38025$$ $$443523600000000$$ $$[2, 2]$$ $$147456$$ $$1.6878$$
23400.c2 23400bk3 $$[0, 0, 0, -162075, -2470250]$$ $$20183398562/11567205$$ $$269839758240000000$$ $$[2]$$ $$294912$$ $$2.0344$$
23400.c1 23400bk4 $$[0, 0, 0, -1872075, -985900250]$$ $$31103978031362/195$$ $$4548960000000$$ $$[2]$$ $$294912$$ $$2.0344$$

## Rank

sage: E.rank()

The elliptic curves in class 23400bk have rank $$1$$.

## Complex multiplication

The elliptic curves in class 23400bk do not have complex multiplication.

## Modular form 23400.2.a.bk

sage: E.q_eigenform(10)

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

## 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.