# Properties

 Label 23232ca Number of curves 4 Conductor 23232 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("23232.dj1")

sage: E.isogeny_class()

## Elliptic curves in class 23232ca

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
23232.dj3 23232ca1 [0, 1, 0, -50497, 4314143]  92160 $$\Gamma_0(N)$$-optimal
23232.dj2 23232ca2 [0, 1, 0, -89217, -3251745] [2, 2] 184320
23232.dj4 23232ca3 [0, 1, 0, 336703, -24973665]  368640
23232.dj1 23232ca4 [0, 1, 0, -1134657, -465127137]  368640

## Rank

sage: E.rank()

The elliptic curves in class 23232ca have rank $$1$$.

## Modular form 23232.2.a.dj

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 