# Properties

 Label 14400.p Number of curves 2 Conductor 14400 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("14400.p1")

sage: E.isogeny_class()

## Elliptic curves in class 14400.p

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
14400.p1 14400fh2 [0, 0, 0, -484500, 129800000] [2] 122880
14400.p2 14400fh1 [0, 0, 0, -28875, 2225000] [2] 61440 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form 14400.2.a.p

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.