# Properties

 Label 14400bt Number of curves 4 Conductor 14400 CM no Rank 2 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("14400.f1")

sage: E.isogeny_class()

## Elliptic curves in class 14400bt

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
14400.f3 14400bt1 [0, 0, 0, -975, -11500] [2] 8192 $$\Gamma_0(N)$$-optimal
14400.f2 14400bt2 [0, 0, 0, -2100, 20000] [2, 2] 16384
14400.f1 14400bt3 [0, 0, 0, -29100, 1910000] [2] 32768
14400.f4 14400bt4 [0, 0, 0, 6900, 146000] [2] 32768

## Rank

sage: E.rank()

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

## Modular form 14400.2.a.f

sage: E.q_eigenform(10)

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

## 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 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.