# Properties

 Label 334620ch Number of curves 4 Conductor 334620 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("334620.ch1")

sage: E.isogeny_class()

## Elliptic curves in class 334620ch

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
334620.ch4 334620ch1 [0, 0, 0, -68952, -6826079]  1866240 $$\Gamma_0(N)$$-optimal
334620.ch3 334620ch2 [0, 0, 0, -152607, 12966694]  3732480
334620.ch2 334620ch3 [0, 0, 0, -677352, 211863301]  5598720
334620.ch1 334620ch4 [0, 0, 0, -10799607, 13660291294]  11197440

## Rank

sage: E.rank()

The elliptic curves in class 334620ch have rank $$0$$.

## Modular form 334620.2.a.ch

sage: E.q_eigenform(10)

$$q + q^{5} + 4q^{7} - q^{11} + 4q^{19} + O(q^{20})$$

## 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. 