# Properties

 Label 23232i Number of curves 4 Conductor 23232 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("23232.s1")

sage: E.isogeny_class()

## Elliptic curves in class 23232i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
23232.s3 23232i1 [0, -1, 0, -42753, -3195135] [2] 92160 $$\Gamma_0(N)$$-optimal
23232.s4 23232i2 [0, -1, 0, 34687, -13556607] [2] 184320
23232.s1 23232i3 [0, -1, 0, -623553, 189003201] [2] 276480
23232.s2 23232i4 [0, -1, 0, -313793, 376531905] [2] 552960

## Rank

sage: E.rank()

The elliptic curves in class 23232i have rank $$0$$.

## Modular form 23232.2.a.s

sage: E.q_eigenform(10)

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

## 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 Cremona numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.