# Properties

 Label 9900l Number of curves $4$ Conductor $9900$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 9900l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9900.e4 9900l1 $$[0, 0, 0, 49200, 15433625]$$ $$72268906496/606436875$$ $$-110523120468750000$$ $$$$ $$55296$$ $$1.9517$$ $$\Gamma_0(N)$$-optimal
9900.e3 9900l2 $$[0, 0, 0, -710175, 212111750]$$ $$13584145739344/1195803675$$ $$3486963516300000000$$ $$$$ $$110592$$ $$2.2983$$
9900.e2 9900l3 $$[0, 0, 0, -3514800, 2538300125]$$ $$-26348629355659264/24169921875$$ $$-4404968261718750000$$ $$$$ $$165888$$ $$2.5010$$
9900.e1 9900l4 $$[0, 0, 0, -56249175, 162376190750]$$ $$6749703004355978704/5671875$$ $$16539187500000000$$ $$$$ $$331776$$ $$2.8476$$

## Rank

sage: E.rank()

The elliptic curves in class 9900l have rank $$1$$.

## Complex multiplication

The elliptic curves in class 9900l do not have complex multiplication.

## Modular form9900.2.a.l

sage: E.q_eigenform(10)

$$q - 2q^{7} - q^{11} - 2q^{13} + 2q^{19} + O(q^{20})$$ ## 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. 