# Properties

 Label 24336i Number of curves $6$ Conductor $24336$ CM no Rank $2$ Graph # Learn more about

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

sage: E.isogeny_class()

## Elliptic curves in class 24336i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
24336.o5 24336i1 $$[0, 0, 0, 1014, 15379]$$ $$2048/3$$ $$-168899700528$$ $$$$ $$18432$$ $$0.83986$$ $$\Gamma_0(N)$$-optimal
24336.o4 24336i2 $$[0, 0, 0, -6591, 153790]$$ $$35152/9$$ $$8107185625344$$ $$[2, 2]$$ $$36864$$ $$1.1864$$
24336.o3 24336i3 $$[0, 0, 0, -37011, -2614430]$$ $$1556068/81$$ $$291858682512384$$ $$[2, 2]$$ $$73728$$ $$1.5330$$
24336.o2 24336i4 $$[0, 0, 0, -97851, 11780314]$$ $$28756228/3$$ $$10809580833792$$ $$$$ $$73728$$ $$1.5330$$
24336.o6 24336i5 $$[0, 0, 0, 23829, -10365446]$$ $$207646/6561$$ $$-47281106567006208$$ $$$$ $$147456$$ $$1.8796$$
24336.o1 24336i6 $$[0, 0, 0, -584571, -172029494]$$ $$3065617154/9$$ $$64857485002752$$ $$$$ $$147456$$ $$1.8796$$

## Rank

sage: E.rank()

The elliptic curves in class 24336i have rank $$2$$.

## Complex multiplication

The elliptic curves in class 24336i do not have complex multiplication.

## Modular form 24336.2.a.i

sage: E.q_eigenform(10)

$$q - 2q^{5} - 4q^{11} - 2q^{17} - 4q^{19} + O(q^{20})$$ ## 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. 