# Properties

 Label 2352.i Number of curves $6$ Conductor $2352$ CM no Rank $0$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 2352.i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2352.i1 2352c5 $$[0, -1, 0, -18832, -988448]$$ $$3065617154/9$$ $$2168506368$$ $$[2]$$ $$3072$$ $$1.0208$$
2352.i2 2352c4 $$[0, -1, 0, -3152, 69168]$$ $$28756228/3$$ $$361417728$$ $$[2]$$ $$1536$$ $$0.67418$$
2352.i3 2352c3 $$[0, -1, 0, -1192, -14720]$$ $$1556068/81$$ $$9758278656$$ $$[2, 2]$$ $$1536$$ $$0.67418$$
2352.i4 2352c2 $$[0, -1, 0, -212, 960]$$ $$35152/9$$ $$271063296$$ $$[2, 2]$$ $$768$$ $$0.32760$$
2352.i5 2352c1 $$[0, -1, 0, 33, 78]$$ $$2048/3$$ $$-5647152$$ $$[2]$$ $$384$$ $$-0.018971$$ $$\Gamma_0(N)$$-optimal
2352.i6 2352c6 $$[0, -1, 0, 768, -60192]$$ $$207646/6561$$ $$-1580841142272$$ $$[2]$$ $$3072$$ $$1.0208$$

## Rank

sage: E.rank()

The elliptic curves in class 2352.i have rank $$0$$.

## Complex multiplication

The elliptic curves in class 2352.i do not have complex multiplication.

## Modular form2352.2.a.i

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 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.