# Properties

 Label 32674d Number of curves 4 Conductor 32674 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("32674.d1")

sage: E.isogeny_class()

## Elliptic curves in class 32674d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
32674.d4 32674d1 [1, 1, 1, -2903, -38483]  60480 $$\Gamma_0(N)$$-optimal
32674.d3 32674d2 [1, 1, 1, -41343, -3252067]  120960
32674.d2 32674d3 [1, 1, 1, -99003, 11947109]  181440
32674.d1 32674d4 [1, 1, 1, -108613, 9475417]  362880

## Rank

sage: E.rank()

The elliptic curves in class 32674d have rank $$0$$.

## Modular form 32674.2.a.d

sage: E.q_eigenform(10)

$$q + q^{2} + 2q^{3} + q^{4} + 2q^{6} - 4q^{7} + q^{8} + q^{9} - 6q^{11} + 2q^{12} - 2q^{13} - 4q^{14} + q^{16} + q^{17} + q^{18} - 4q^{19} + O(q^{20})$$

## 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. 