# Properties

 Label 20808.i Number of curves $6$ Conductor $20808$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("i1")

sage: E.isogeny_class()

## Elliptic curves in class 20808.i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
20808.i1 20808l5 $$[0, 0, 0, -999651, 384697726]$$ $$3065617154/9$$ $$324334776748032$$ $$[2]$$ $$163840$$ $$2.0137$$
20808.i2 20808l3 $$[0, 0, 0, -167331, -26343506]$$ $$28756228/3$$ $$54055796124672$$ $$[2]$$ $$81920$$ $$1.6671$$
20808.i3 20808l4 $$[0, 0, 0, -63291, 5846470]$$ $$1556068/81$$ $$1459506495366144$$ $$[2, 2]$$ $$81920$$ $$1.6671$$
20808.i4 20808l2 $$[0, 0, 0, -11271, -343910]$$ $$35152/9$$ $$40541847093504$$ $$[2, 2]$$ $$40960$$ $$1.3206$$
20808.i5 20808l1 $$[0, 0, 0, 1734, -34391]$$ $$2048/3$$ $$-844621814448$$ $$[2]$$ $$20480$$ $$0.97399$$ $$\Gamma_0(N)$$-optimal
20808.i6 20808l6 $$[0, 0, 0, 40749, 23179534]$$ $$207646/6561$$ $$-236440052249315328$$ $$[2]$$ $$163840$$ $$2.0137$$

## Rank

sage: E.rank()

The elliptic curves in class 20808.i have rank $$0$$.

## Complex multiplication

The elliptic curves in class 20808.i do not have complex multiplication.

## Modular form 20808.2.a.i

sage: E.q_eigenform(10)

$$q - 2q^{5} + 4q^{11} - 2q^{13} - 4q^{19} + O(q^{20})$$

## 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 LMFDB numbering.

$$\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 8 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 2 & 4 & 1 & 2 & 4 & 2 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 8 & 4 & 4 & 2 & 1 & 8 \\ 4 & 8 & 2 & 4 & 8 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels.