# Properties

 Label 110400.cz Number of curves $6$ Conductor $110400$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("110400.cz1")

sage: E.isogeny_class()

## Elliptic curves in class 110400.cz

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
110400.cz1 110400fl4 [0, -1, 0, -176640033, -903552768063] [2] 7077888
110400.cz2 110400fl6 [0, -1, 0, -41328033, 87610415937] [2] 14155776
110400.cz3 110400fl3 [0, -1, 0, -11328033, -13339584063] [2, 2] 7077888
110400.cz4 110400fl2 [0, -1, 0, -11040033, -14115168063] [2, 2] 3538944
110400.cz5 110400fl1 [0, -1, 0, -672033, -232416063] [2] 1769472 $$\Gamma_0(N)$$-optimal
110400.cz6 110400fl5 [0, -1, 0, 14063967, -64656816063] [2] 14155776

## Rank

sage: E.rank()

The elliptic curves in class 110400.cz have rank $$0$$.

## Modular form 110400.2.a.cz

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.