# Properties

 Label 334620l Number of curves $4$ Conductor $334620$ CM no Rank $2$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 334620l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
334620.l4 334620l1 $$[0, 0, 0, 332592, 271261393]$$ $$72268906496/606436875$$ $$-34142335525545390000$$ $$[2]$$ $$5308416$$ $$2.4295$$ $$\Gamma_0(N)$$-optimal
334620.l3 334620l2 $$[0, 0, 0, -4800783, 3728076118]$$ $$13584145739344/1195803675$$ $$1077178040521503148800$$ $$[2]$$ $$10616832$$ $$2.7760$$
334620.l2 334620l3 $$[0, 0, 0, -23760048, 44613162997]$$ $$-26348629355659264/24169921875$$ $$-1360764188824218750000$$ $$[2]$$ $$15925248$$ $$2.9788$$
334620.l1 334620l4 $$[0, 0, 0, -380244423, 2853923928622]$$ $$6749703004355978704/5671875$$ $$5109215940972000000$$ $$[2]$$ $$31850496$$ $$3.3253$$

## Rank

sage: E.rank()

The elliptic curves in class 334620l have rank $$2$$.

## Complex multiplication

The elliptic curves in class 334620l do not have complex multiplication.

## Modular form 334620.2.a.l

sage: E.q_eigenform(10)

$$q - q^{5} - 2q^{7} + q^{11} - 2q^{19} + O(q^{20})$$

## 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.