# Properties

 Label 11200p Number of curves $4$ Conductor $11200$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("11200.bt1")

sage: E.isogeny_class()

## Elliptic curves in class 11200p

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
11200.bt4 11200p1 [0, 0, 0, 3700, -138000]  18432 $$\Gamma_0(N)$$-optimal
11200.bt3 11200p2 [0, 0, 0, -28300, -1482000] [2, 2] 36864
11200.bt1 11200p3 [0, 0, 0, -428300, -107882000]  73728
11200.bt2 11200p4 [0, 0, 0, -140300, 18902000]  73728

## Rank

sage: E.rank()

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

## Modular form 11200.2.a.bt

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. 