# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("14400.cj1")

sage: E.isogeny_class()

## Elliptic curves in class 14400.cj

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
14400.cj1 14400y7 [0, 0, 0, -31104300, 66769598000] [2] 393216
14400.cj2 14400y5 [0, 0, 0, -1944300, 1042958000] [2, 2] 196608
14400.cj3 14400y8 [0, 0, 0, -1584300, 1441118000] [2] 393216
14400.cj4 14400y3 [0, 0, 0, -1152300, -476098000] [2] 98304
14400.cj5 14400y4 [0, 0, 0, -144300, 9758000] [2, 2] 98304
14400.cj6 14400y2 [0, 0, 0, -72300, -7378000] [2, 2] 49152
14400.cj7 14400y1 [0, 0, 0, -300, -322000] [2] 24576 $$\Gamma_0(N)$$-optimal
14400.cj8 14400y6 [0, 0, 0, 503700, 73262000] [2] 196608

## Rank

sage: E.rank()

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

## Modular form 14400.2.a.cj

sage: E.q_eigenform(10)

$$q - 4q^{11} - 2q^{13} + 2q^{17} - 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 16 & 4 & 8 & 16 & 8 \\ 2 & 1 & 2 & 8 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 16 & 4 & 8 & 16 & 8 \\ 16 & 8 & 16 & 1 & 4 & 2 & 4 & 8 \\ 4 & 2 & 4 & 4 & 1 & 2 & 4 & 2 \\ 8 & 4 & 8 & 2 & 2 & 1 & 2 & 4 \\ 16 & 8 & 16 & 4 & 4 & 2 & 1 & 8 \\ 8 & 4 & 8 & 8 & 2 & 4 & 8 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.