# Properties

 Label 2200.i Number of curves $2$ Conductor $2200$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("i1")

E.isogeny_class()

## Elliptic curves in class 2200.i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2200.i1 2200c2 $$[0, -1, 0, -228, -748]$$ $$41141648/14641$$ $$468512000$$ $$[2]$$ $$768$$ $$0.36476$$
2200.i2 2200c1 $$[0, -1, 0, -203, -1048]$$ $$464857088/121$$ $$242000$$ $$[2]$$ $$384$$ $$0.018186$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 2200.i have rank $$0$$.

## Complex multiplication

The elliptic curves in class 2200.i do not have complex multiplication.

## Modular form2200.2.a.i

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.