# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("23232.cv1")

sage: E.isogeny_class()

## Elliptic curves in class 23232dm

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
23232.cv3 23232dm1 [0, 1, 0, -42753, 3195135] [2] 92160 $$\Gamma_0(N)$$-optimal
23232.cv4 23232dm2 [0, 1, 0, 34687, 13556607] [2] 184320
23232.cv1 23232dm3 [0, 1, 0, -623553, -189003201] [2] 276480
23232.cv2 23232dm4 [0, 1, 0, -313793, -376531905] [2] 552960

## Rank

sage: E.rank()

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

## Modular form 23232.2.a.cv

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.