# Properties

 Label 2304.k Number of curves $2$ Conductor $2304$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("k1")

E.isogeny_class()

## Elliptic curves in class 2304.k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2304.k1 2304d1 $$[0, 0, 0, -210, 1168]$$ $$2744000/9$$ $$3359232$$ $$[2]$$ $$512$$ $$0.11759$$ $$\Gamma_0(N)$$-optimal
2304.k2 2304d2 $$[0, 0, 0, -120, 2176]$$ $$-8000/81$$ $$-1934917632$$ $$[2]$$ $$1024$$ $$0.46417$$

## Rank

sage: E.rank()

The elliptic curves in class 2304.k have rank $$0$$.

## Complex multiplication

The elliptic curves in class 2304.k do not have complex multiplication.

## Modular form2304.2.a.k

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.