# Properties

 Label 23232dr Number of curves 2 Conductor 23232 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("23232.ch1")

sage: E.isogeny_class()

## Elliptic curves in class 23232dr

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
23232.ch2 23232dr1 [0, 1, 0, 1291, -9429] [2] 23040 $$\Gamma_0(N)$$-optimal
23232.ch1 23232dr2 [0, 1, 0, -5969, -86385] [2] 46080

## Rank

sage: E.rank()

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

## Modular form 23232.2.a.ch

sage: E.q_eigenform(10)

$$q + q^{3} - 2q^{5} - 2q^{7} + q^{9} - 2q^{13} - 2q^{15} - 4q^{17} + 6q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.