# Properties

 Label 2304.c Number of curves $2$ Conductor $2304$ CM $$\Q(\sqrt{-1})$$ Rank $1$ Graph # Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("c1")

sage: E.isogeny_class()

## Elliptic curves in class 2304.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality CM discriminant
2304.c1 2304b1 $$[0, 0, 0, -6, 0]$$ $$1728$$ $$13824$$ $$$$ $$128$$ $$-0.51602$$ $$\Gamma_0(N)$$-optimal $$-4$$
2304.c2 2304b2 $$[0, 0, 0, 24, 0]$$ $$1728$$ $$-884736$$ $$$$ $$256$$ $$-0.16945$$   $$-4$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form2304.2.a.c

sage: E.q_eigenform(10)

$$q - 2q^{5} - 4q^{13} + 8q^{17} + O(q^{20})$$ ## 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. 