# Properties

 Label 33813.i Number of curves $6$ Conductor $33813$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("33813.i1")

sage: E.isogeny_class()

## Elliptic curves in class 33813.i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
33813.i1 33813n6 [1, -1, 0, -52472628, 146291618079] [2] 2359296
33813.i2 33813n4 [1, -1, 0, -3612843, 1793689920] [2, 2] 1179648
33813.i3 33813n2 [1, -1, 0, -1414998, -626137425] [2, 2] 589824
33813.i4 33813n1 [1, -1, 0, -1401993, -638598816] [2] 294912 $$\Gamma_0(N)$$-optimal
33813.i5 33813n3 [1, -1, 0, 574767, -2248591806] [2] 1179648
33813.i6 33813n5 [1, -1, 0, 10081422, 12138337701] [2] 2359296

## Rank

sage: E.rank()

The elliptic curves in class 33813.i have rank $$1$$.

## Modular form 33813.2.a.i

sage: E.q_eigenform(10)

$$q + q^{2} - q^{4} - 2q^{5} - 3q^{8} - 2q^{10} + 4q^{11} + q^{13} - q^{16} - 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 8 & 4 \\ 2 & 1 & 2 & 4 & 4 & 2 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 2 & 4 & 8 & 8 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.