# Properties

 Label 2304.a Number of curves $2$ Conductor $2304$ CM $$\Q(\sqrt{-1})$$ Rank $1$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("a1")

E.isogeny_class()

## Elliptic curves in class 2304.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality CM discriminant
2304.a1 2304p2 $$[0, 0, 0, -72, 0]$$ $$1728$$ $$23887872$$ $$[2]$$ $$512$$ $$0.10521$$   $$-4$$
2304.a2 2304p1 $$[0, 0, 0, 18, 0]$$ $$1728$$ $$-373248$$ $$[2]$$ $$256$$ $$-0.24137$$ $$\Gamma_0(N)$$-optimal $$-4$$

## Rank

sage: E.rank()

The elliptic curves in class 2304.a have rank $$1$$.

## Complex multiplication

Each elliptic curve in class 2304.a has complex multiplication by an order in the imaginary quadratic field $$\Q(\sqrt{-1})$$.

## Modular form2304.2.a.a

sage: E.q_eigenform(10)

$$q - 4 q^{5} + 4 q^{13} + 2 q^{17} + O(q^{20})$$

## 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 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.