# Properties

 Label 34650dc Number of curves 4 Conductor 34650 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("34650.dm1")

sage: E.isogeny_class()

## Elliptic curves in class 34650dc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
34650.dm3 34650dc1 [1, -1, 1, -12605, -10596603] [2] 331776 $$\Gamma_0(N)$$-optimal
34650.dm2 34650dc2 [1, -1, 1, -804605, -275124603] [2] 663552
34650.dm4 34650dc3 [1, -1, 1, 113395, 285503397] [2] 995328
34650.dm1 34650dc4 [1, -1, 1, -5876105, 5328662397] [2] 1990656

## Rank

sage: E.rank()

The elliptic curves in class 34650dc have rank $$0$$.

## Modular form 34650.2.a.dm

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} - q^{7} + q^{8} + q^{11} + 4q^{13} - q^{14} + q^{16} - 4q^{19} + O(q^{20})$$

## 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.