# Properties

 Label 14400bu Number of curves 4 Conductor 14400 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("14400.j1")

sage: E.isogeny_class()

## Elliptic curves in class 14400bu

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
14400.j3 14400bu1 [0, 0, 0, -202575, 35093500] [2] 73728 $$\Gamma_0(N)$$-optimal
14400.j2 14400bu2 [0, 0, 0, -203700, 34684000] [2, 2] 147456
14400.j1 14400bu3 [0, 0, 0, -446700, -63974000] [2] 294912
14400.j4 14400bu4 [0, 0, 0, 21300, 107134000] [2] 294912

## Rank

sage: E.rank()

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

## Modular form 14400.2.a.j

sage: E.q_eigenform(10)

$$q - 4q^{7} - 4q^{11} + 6q^{13} + 2q^{17} + 4q^{19} + O(q^{20})$$

## 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 Cremona numbering.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.