# Properties

 Label 9408cz Number of curves $6$ Conductor $9408$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("cz1")

sage: E.isogeny_class()

## Elliptic curves in class 9408cz

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9408.cc5 9408cz1 $$[0, 1, 0, 131, 755]$$ $$2048/3$$ $$-361417728$$ $$[2]$$ $$3072$$ $$0.32760$$ $$\Gamma_0(N)$$-optimal
9408.cc4 9408cz2 $$[0, 1, 0, -849, 6831]$$ $$35152/9$$ $$17348050944$$ $$[2, 2]$$ $$6144$$ $$0.67418$$
9408.cc3 9408cz3 $$[0, 1, 0, -4769, -122529]$$ $$1556068/81$$ $$624529833984$$ $$[2, 2]$$ $$12288$$ $$1.0208$$
9408.cc2 9408cz4 $$[0, 1, 0, -12609, 540735]$$ $$28756228/3$$ $$23130734592$$ $$[2]$$ $$12288$$ $$1.0208$$
9408.cc1 9408cz5 $$[0, 1, 0, -75329, -7982913]$$ $$3065617154/9$$ $$138784407552$$ $$[2]$$ $$24576$$ $$1.3673$$
9408.cc6 9408cz6 $$[0, 1, 0, 3071, -478465]$$ $$207646/6561$$ $$-101173833105408$$ $$[2]$$ $$24576$$ $$1.3673$$

## Rank

sage: E.rank()

The elliptic curves in class 9408cz have rank $$0$$.

## Complex multiplication

The elliptic curves in class 9408cz do not have complex multiplication.

## Modular form9408.2.a.cz

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 Cremona numbering.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.