# Properties

 Label 14400.n Number of curves $4$ Conductor $14400$ CM $$\Q(\sqrt{-3})$$ Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("n1")

sage: E.isogeny_class()

## Elliptic curves in class 14400.n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality CM discriminant
14400.n1 14400cz4 $$[0, 0, 0, -13500, 594000]$$ $$54000$$ $$5038848000000$$ $$[2]$$ $$27648$$ $$1.2318$$   $$-12$$
14400.n2 14400cz2 $$[0, 0, 0, -1500, -22000]$$ $$54000$$ $$6912000000$$ $$[2]$$ $$9216$$ $$0.68245$$   $$-12$$
14400.n3 14400cz1 $$[0, 0, 0, 0, -1000]$$ $$0$$ $$-432000000$$ $$[2]$$ $$4608$$ $$0.33588$$ $$\Gamma_0(N)$$-optimal $$-3$$
14400.n4 14400cz3 $$[0, 0, 0, 0, 27000]$$ $$0$$ $$-314928000000$$ $$[2]$$ $$13824$$ $$0.88518$$   $$-3$$

## Rank

sage: E.rank()

The elliptic curves in class 14400.n have rank $$0$$.

## Complex multiplication

Each elliptic curve in class 14400.n has complex multiplication by an order in the imaginary quadratic field $$\Q(\sqrt{-3})$$.

## Modular form 14400.2.a.n

sage: E.q_eigenform(10)

$$q - 4q^{7} + 2q^{13} + 8q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.