# Properties

 Label 14400dp Number of curves 8 Conductor 14400 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("14400.cz1")

sage: E.isogeny_class()

## Elliptic curves in class 14400dp

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
14400.cz7 14400dp1 [0, 0, 0, -300, 322000] [2] 24576 $$\Gamma_0(N)$$-optimal
14400.cz6 14400dp2 [0, 0, 0, -72300, 7378000] [2, 2] 49152
14400.cz5 14400dp3 [0, 0, 0, -144300, -9758000] [2, 2] 98304
14400.cz4 14400dp4 [0, 0, 0, -1152300, 476098000] [2] 98304
14400.cz2 14400dp5 [0, 0, 0, -1944300, -1042958000] [2, 2] 196608
14400.cz8 14400dp6 [0, 0, 0, 503700, -73262000] [2] 196608
14400.cz1 14400dp7 [0, 0, 0, -31104300, -66769598000] [2] 393216
14400.cz3 14400dp8 [0, 0, 0, -1584300, -1441118000] [2] 393216

## Rank

sage: E.rank()

The elliptic curves in class 14400dp have rank $$1$$.

## Modular form 14400.2.a.cz

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 Cremona numbering.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.