# Properties

 Label 14400.g Number of curves 4 Conductor 14400 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("14400.g1")

sage: E.isogeny_class()

## Elliptic curves in class 14400.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
14400.g1 14400eh3 [0, 0, 0, -96300, -11502000] [2] 49152
14400.g2 14400eh2 [0, 0, 0, -6300, -162000] [2, 2] 24576
14400.g3 14400eh1 [0, 0, 0, -1800, 27000] [2] 12288 $$\Gamma_0(N)$$-optimal
14400.g4 14400eh4 [0, 0, 0, 11700, -918000] [2] 49152

## Rank

sage: E.rank()

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

## Modular form 14400.2.a.g

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.