# Properties

 Label 14400.k Number of curves $4$ Conductor $14400$ CM no Rank $2$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("k1")

sage: E.isogeny_class()

## Elliptic curves in class 14400.k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14400.k1 14400bs4 $$[0, 0, 0, -194700, 33046000]$$ $$546718898/405$$ $$604661760000000$$ $$$$ $$98304$$ $$1.7700$$
14400.k2 14400bs3 $$[0, 0, 0, -122700, -16346000]$$ $$136835858/1875$$ $$2799360000000000$$ $$$$ $$98304$$ $$1.7700$$
14400.k3 14400bs2 $$[0, 0, 0, -14700, 286000]$$ $$470596/225$$ $$167961600000000$$ $$[2, 2]$$ $$49152$$ $$1.4234$$
14400.k4 14400bs1 $$[0, 0, 0, 3300, 34000]$$ $$21296/15$$ $$-2799360000000$$ $$$$ $$24576$$ $$1.0769$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 14400.k have rank $$2$$.

## Complex multiplication

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

## Modular form 14400.2.a.k

sage: E.q_eigenform(10)

$$q - 4q^{7} - 6q^{13} - 2q^{17} - 4q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 