# Properties

 Label 12168.j Number of curves $6$ Conductor $12168$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("j1")

sage: E.isogeny_class()

## Elliptic curves in class 12168.j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
12168.j1 12168q5 $$[0, 0, 0, -584571, 172029494]$$ $$3065617154/9$$ $$64857485002752$$ $$[2]$$ $$73728$$ $$1.8796$$
12168.j2 12168q3 $$[0, 0, 0, -97851, -11780314]$$ $$28756228/3$$ $$10809580833792$$ $$[2]$$ $$36864$$ $$1.5330$$
12168.j3 12168q4 $$[0, 0, 0, -37011, 2614430]$$ $$1556068/81$$ $$291858682512384$$ $$[2, 2]$$ $$36864$$ $$1.5330$$
12168.j4 12168q2 $$[0, 0, 0, -6591, -153790]$$ $$35152/9$$ $$8107185625344$$ $$[2, 2]$$ $$18432$$ $$1.1864$$
12168.j5 12168q1 $$[0, 0, 0, 1014, -15379]$$ $$2048/3$$ $$-168899700528$$ $$[2]$$ $$9216$$ $$0.83986$$ $$\Gamma_0(N)$$-optimal
12168.j6 12168q6 $$[0, 0, 0, 23829, 10365446]$$ $$207646/6561$$ $$-47281106567006208$$ $$[2]$$ $$73728$$ $$1.8796$$

## Rank

sage: E.rank()

The elliptic curves in class 12168.j have rank $$1$$.

## Complex multiplication

The elliptic curves in class 12168.j do not have complex multiplication.

## Modular form 12168.2.a.j

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 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.