# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("14400.k1")

sage: E.isogeny_class()

## Elliptic curves in class 14400.k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
14400.k1 14400bs4 [0, 0, 0, -194700, 33046000]  98304
14400.k2 14400bs3 [0, 0, 0, -122700, -16346000]  98304
14400.k3 14400bs2 [0, 0, 0, -14700, 286000] [2, 2] 49152
14400.k4 14400bs1 [0, 0, 0, 3300, 34000]  24576 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## 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. 