# Properties

 Label 14400.ez Number of curves 8 Conductor 14400 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("14400.ez1")

sage: E.isogeny_class()

## Elliptic curves in class 14400.ez

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
14400.ez1 14400bo8 [0, 0, 0, -76802700, 259067446000] [2] 884736
14400.ez2 14400bo7 [0, 0, 0, -6530700, 874294000] [2] 884736
14400.ez3 14400bo6 [0, 0, 0, -4802700, 4043446000] [2, 2] 442368
14400.ez4 14400bo4 [0, 0, 0, -4154700, -3259514000] [2] 294912
14400.ez5 14400bo5 [0, 0, 0, -986700, 324934000] [2] 294912
14400.ez6 14400bo2 [0, 0, 0, -266700, -48026000] [2, 2] 147456
14400.ez7 14400bo3 [0, 0, 0, -194700, 108214000] [2] 221184
14400.ez8 14400bo1 [0, 0, 0, 21300, -3674000] [2] 73728 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form 14400.2.a.ez

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrrrrrr} 1 & 4 & 2 & 12 & 3 & 6 & 4 & 12 \\ 4 & 1 & 2 & 3 & 12 & 6 & 4 & 12 \\ 2 & 2 & 1 & 6 & 6 & 3 & 2 & 6 \\ 12 & 3 & 6 & 1 & 4 & 2 & 12 & 4 \\ 3 & 12 & 6 & 4 & 1 & 2 & 12 & 4 \\ 6 & 6 & 3 & 2 & 2 & 1 & 6 & 2 \\ 4 & 4 & 2 & 12 & 12 & 6 & 1 & 3 \\ 12 & 12 & 6 & 4 & 4 & 2 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.