# Properties

 Label 23232dc Number of curves 4 Conductor 23232 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("23232.l1")

sage: E.isogeny_class()

## Elliptic curves in class 23232dc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
23232.l3 23232dc1 [0, -1, 0, -5969, -169167] [2] 30720 $$\Gamma_0(N)$$-optimal
23232.l2 23232dc2 [0, -1, 0, -15649, 529729] [2, 2] 61440
23232.l4 23232dc3 [0, -1, 0, 42431, 3491809] [2] 122880
23232.l1 23232dc4 [0, -1, 0, -228609, 42142113] [2] 122880

## Rank

sage: E.rank()

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

## Modular form 23232.2.a.l

sage: E.q_eigenform(10)

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

## 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.