# Properties

 Label 20184.i Number of curves $6$ Conductor $20184$ CM no Rank $0$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 20184.i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
20184.i1 20184f5 $$[0, 1, 0, -323224, -70837648]$$ $$3065617154/9$$ $$10963783452672$$ $$[2]$$ $$96768$$ $$1.7314$$
20184.i2 20184f4 $$[0, 1, 0, -54104, 4825440]$$ $$28756228/3$$ $$1827297242112$$ $$[2]$$ $$48384$$ $$1.3849$$
20184.i3 20184f3 $$[0, 1, 0, -20464, -1081744]$$ $$1556068/81$$ $$49337025537024$$ $$[2, 2]$$ $$48384$$ $$1.3849$$
20184.i4 20184f2 $$[0, 1, 0, -3644, 62016]$$ $$35152/9$$ $$1370472931584$$ $$[2, 2]$$ $$24192$$ $$1.0383$$
20184.i5 20184f1 $$[0, 1, 0, 561, 6510]$$ $$2048/3$$ $$-28551519408$$ $$[2]$$ $$12096$$ $$0.69172$$ $$\Gamma_0(N)$$-optimal
20184.i6 20184f6 $$[0, 1, 0, 13176, -4257360]$$ $$207646/6561$$ $$-7992598136997888$$ $$[2]$$ $$96768$$ $$1.7314$$

## Rank

sage: E.rank()

The elliptic curves in class 20184.i have rank $$0$$.

## Complex multiplication

The elliptic curves in class 20184.i do not have complex multiplication.

## Modular form 20184.2.a.i

sage: E.q_eigenform(10)

$$q + q^{3} - 2q^{5} + q^{9} - 4q^{11} - 2q^{13} - 2q^{15} - 2q^{17} + 4q^{19} + O(q^{20})$$

## 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.