# Properties

 Label 92400.cw Number of curves $6$ Conductor $92400$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("cw1")

sage: E.isogeny_class()

## Elliptic curves in class 92400.cw

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92400.cw1 92400be6 $$[0, -1, 0, -12806640008, 557833047898512]$$ $$7259042500647479362626220802/12006225$$ $$384199200000000$$ $$[2]$$ $$56623104$$ $$3.9331$$
92400.cw2 92400be4 $$[0, -1, 0, -800415008, 8716341298512]$$ $$3544454449806874081077604/144149438750625$$ $$2306391020010000000000$$ $$[2, 2]$$ $$28311552$$ $$3.5865$$
92400.cw3 92400be5 $$[0, -1, 0, -799190008, 8744349698512]$$ $$-1764102724103262766456802/11303622506742021225$$ $$-361715920215744679200000000$$ $$[2]$$ $$56623104$$ $$3.9331$$
92400.cw4 92400be3 $$[0, -1, 0, -81040008, -51837451488]$$ $$3678765970528905177604/2056287578994061875$$ $$32900601263904990000000000$$ $$[2]$$ $$28311552$$ $$3.5865$$
92400.cw5 92400be2 $$[0, -1, 0, -50102508, 135767548512]$$ $$3477299736386222510416/22070630703515625$$ $$88282522814062500000000$$ $$[2, 2]$$ $$14155776$$ $$3.2400$$
92400.cw6 92400be1 $$[0, -1, 0, -1274383, 4615204762]$$ $$-915553975060166656/36269989013671875$$ $$-9067497253417968750000$$ $$[2]$$ $$7077888$$ $$2.8934$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 92400.cw have rank $$1$$.

## Complex multiplication

The elliptic curves in class 92400.cw do not have complex multiplication.

## Modular form 92400.2.a.cw

sage: E.q_eigenform(10)

$$q - q^{3} + q^{7} + q^{9} + q^{11} - 6q^{13} - 2q^{17} + 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.