# Properties

 Label 32448.ch Number of curves $6$ Conductor $32448$ CM no Rank $0$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 32448.ch

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32448.ch1 32448bh6 $$[0, 1, 0, -259809, -51058305]$$ $$3065617154/9$$ $$5693935583232$$ $$[2]$$ $$147456$$ $$1.6768$$
32448.ch2 32448bh4 $$[0, 1, 0, -43489, 3475967]$$ $$28756228/3$$ $$948989263872$$ $$[2]$$ $$73728$$ $$1.3303$$
32448.ch3 32448bh3 $$[0, 1, 0, -16449, -780129]$$ $$1556068/81$$ $$25622710124544$$ $$[2, 2]$$ $$73728$$ $$1.3303$$
32448.ch4 32448bh2 $$[0, 1, 0, -2929, 44591]$$ $$35152/9$$ $$711741947904$$ $$[2, 2]$$ $$36864$$ $$0.98370$$
32448.ch5 32448bh1 $$[0, 1, 0, 451, 4707]$$ $$2048/3$$ $$-14827957248$$ $$[2]$$ $$18432$$ $$0.63712$$ $$\Gamma_0(N)$$-optimal
32448.ch6 32448bh5 $$[0, 1, 0, 10591, -3067713]$$ $$207646/6561$$ $$-4150879040176128$$ $$[2]$$ $$147456$$ $$1.6768$$

## Rank

sage: E.rank()

The elliptic curves in class 32448.ch have rank $$0$$.

## Complex multiplication

The elliptic curves in class 32448.ch do not have complex multiplication.

## Modular form 32448.2.a.ch

sage: E.q_eigenform(10)

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

## 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.