# Properties

 Label 14400cz Number of curves 4 Conductor 14400 CM -3 Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("14400.n1")

sage: E.isogeny_class()

## Elliptic curves in class 14400cz

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
14400.n3 14400cz1 [0, 0, 0, 0, -1000]  4608 $$\Gamma_0(N)$$-optimal
14400.n2 14400cz2 [0, 0, 0, -1500, -22000]  9216
14400.n4 14400cz3 [0, 0, 0, 0, 27000]  13824
14400.n1 14400cz4 [0, 0, 0, -13500, 594000]  27648

## Rank

sage: E.rank()

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

## 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 Cremona numbering.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 