# Properties

 Label 23232.dr Number of curves 4 Conductor 23232 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("23232.dr1")

sage: E.isogeny_class()

## Elliptic curves in class 23232.dr

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
23232.dr1 23232dq4 [0, 1, 0, -340897, 76495967]  184320
23232.dr2 23232dq3 [0, 1, 0, -50497, -2713537]  184320
23232.dr3 23232dq2 [0, 1, 0, -21457, 1172015] [2, 2] 92160
23232.dr4 23232dq1 [0, 1, 0, 323, 61235]  46080 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form 23232.2.a.dr

sage: E.q_eigenform(10)

$$q + q^{3} + 2q^{5} + 4q^{7} + q^{9} + 6q^{13} + 2q^{15} - 6q^{17} + 8q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 