# Properties

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

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("h1")

sage: E.isogeny_class()

## Elliptic curves in class 2304.h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality CM discriminant
2304.h1 2304k2 $$[0, 0, 0, -120, -448]$$ $$8000$$ $$23887872$$ $$[2]$$ $$384$$ $$0.14533$$   $$-8$$
2304.h2 2304k1 $$[0, 0, 0, -30, 56]$$ $$8000$$ $$373248$$ $$[2]$$ $$192$$ $$-0.20124$$ $$\Gamma_0(N)$$-optimal $$-8$$

## Rank

sage: E.rank()

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

## Complex multiplication

Each elliptic curve in class 2304.h has complex multiplication by an order in the imaginary quadratic field $$\Q(\sqrt{-2})$$.

## Modular form2304.2.a.h

sage: E.q_eigenform(10)

$$q - 6q^{11} + 6q^{17} + 2q^{19} + O(q^{20})$$

## 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.