# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("n1")

sage: E.isogeny_class()

## Elliptic curves in class 11200n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
11200.ca4 11200n1 [0, 0, 0, 100, 2000]  4096 $$\Gamma_0(N)$$-optimal
11200.ca3 11200n2 [0, 0, 0, -1900, 30000] [2, 2] 8192
11200.ca2 11200n3 [0, 0, 0, -5900, -138000]  16384
11200.ca1 11200n4 [0, 0, 0, -29900, 1990000]  16384

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 11200n do not have complex multiplication.

## Modular form 11200.2.a.n

sage: E.q_eigenform(10)

$$q + q^{7} - 3q^{9} + 4q^{11} + 2q^{13} + 6q^{17} - 8q^{19} + O(q^{20})$$

## 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 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. 