# Properties

 Label 110400.gx Number of curves $6$ Conductor $110400$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("110400.gx1")

sage: E.isogeny_class()

## Elliptic curves in class 110400.gx

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
110400.gx1 110400dq4 [0, 1, 0, -176640033, 903552768063] [2] 7077888
110400.gx2 110400dq6 [0, 1, 0, -41328033, -87610415937] [2] 14155776
110400.gx3 110400dq3 [0, 1, 0, -11328033, 13339584063] [2, 2] 7077888
110400.gx4 110400dq2 [0, 1, 0, -11040033, 14115168063] [2, 2] 3538944
110400.gx5 110400dq1 [0, 1, 0, -672033, 232416063] [2] 1769472 $$\Gamma_0(N)$$-optimal
110400.gx6 110400dq5 [0, 1, 0, 14063967, 64656816063] [2] 14155776

## Rank

sage: E.rank()

The elliptic curves in class 110400.gx have rank $$1$$.

## Modular form 110400.2.a.gx

sage: E.q_eigenform(10)

$$q + q^{3} + q^{9} - 4q^{11} - 2q^{13} + 6q^{17} - 4q^{19} + O(q^{20})$$

## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.