# Properties

 Label 11200bu Number of curves $4$ Conductor $11200$ CM no Rank $0$ Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("11200.bq1")

sage: E.isogeny_class()

## Elliptic curves in class 11200bu

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
11200.bq4 11200bu1 [0, 0, 0, 3700, 138000] [2] 18432 $$\Gamma_0(N)$$-optimal
11200.bq3 11200bu2 [0, 0, 0, -28300, 1482000] [2, 2] 36864
11200.bq2 11200bu3 [0, 0, 0, -140300, -18902000] [2] 73728
11200.bq1 11200bu4 [0, 0, 0, -428300, 107882000] [2] 73728

## Rank

sage: E.rank()

The elliptic curves in class 11200bu have rank $$0$$.

## Modular form 11200.2.a.bq

sage: E.q_eigenform(10)

$$q - q^{7} - 3q^{9} + 4q^{11} - 6q^{13} - 2q^{17} + O(q^{20})$$

## 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 Cremona 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 Cremona labels.