# Properties

 Label 14400fh Number of curves $2$ Conductor $14400$ CM no Rank $0$ Graph # Learn more

Show commands: SageMath
sage: E = EllipticCurve("fh1")

sage: E.isogeny_class()

## Elliptic curves in class 14400fh

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14400.p2 14400fh1 $$[0, 0, 0, -28875, 2225000]$$ $$-29218112/6561$$ $$-597871125000000$$ $$$$ $$61440$$ $$1.5555$$ $$\Gamma_0(N)$$-optimal
14400.p1 14400fh2 $$[0, 0, 0, -484500, 129800000]$$ $$2156689088/81$$ $$472392000000000$$ $$$$ $$122880$$ $$1.9021$$

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 14400fh do not have complex multiplication.

## Modular form 14400.2.a.fh

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 Cremona 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 Cremona labels. 