# Properties

 Label 11200.cz Number of curves 6 Conductor 11200 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("11200.cz1")

sage: E.isogeny_class()

## Elliptic curves in class 11200.cz

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
11200.cz1 11200co6 [0, -1, 0, -4368833, 3516221537] [2] 165888
11200.cz2 11200co5 [0, -1, 0, -272833, 55101537] [2] 82944
11200.cz3 11200co4 [0, -1, 0, -56833, 4293537] [2] 55296
11200.cz4 11200co2 [0, -1, 0, -16833, -834463] [2] 18432
11200.cz5 11200co1 [0, -1, 0, -833, -18463] [2] 9216 $$\Gamma_0(N)$$-optimal
11200.cz6 11200co3 [0, -1, 0, 7167, 389537] [2] 27648

## Rank

sage: E.rank()

The elliptic curves in class 11200.cz have rank $$1$$.

## Modular form 11200.2.a.cz

sage: E.q_eigenform(10)

$$q + 2q^{3} + q^{7} + q^{9} - 4q^{13} - 6q^{17} + 2q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 9 & 18 & 6 \\ 2 & 1 & 6 & 18 & 9 & 3 \\ 3 & 6 & 1 & 3 & 6 & 2 \\ 9 & 18 & 3 & 1 & 2 & 6 \\ 18 & 9 & 6 & 2 & 1 & 3 \\ 6 & 3 & 2 & 6 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.