# Properties

 Label 14400.fd Number of curves 4 Conductor 14400 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("14400.fd1")

sage: E.isogeny_class()

## Elliptic curves in class 14400.fd

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
14400.fd1 14400bp3 [0, 0, 0, -96300, 11502000]  49152
14400.fd2 14400bp2 [0, 0, 0, -6300, 162000] [2, 2] 24576
14400.fd3 14400bp1 [0, 0, 0, -1800, -27000]  12288 $$\Gamma_0(N)$$-optimal
14400.fd4 14400bp4 [0, 0, 0, 11700, 918000]  49152

## Rank

sage: E.rank()

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

## Modular form 14400.2.a.fd

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 