# Properties

 Label 3192.i Number of curves $4$ Conductor $3192$ CM no Rank $0$ Graph # Related objects

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

E.isogeny_class()

## Elliptic curves in class 3192.i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3192.i1 3192a3 $$[0, -1, 0, -1232, 17052]$$ $$202119559492/136857$$ $$140141568$$ $$$$ $$2048$$ $$0.50119$$
3192.i2 3192a2 $$[0, -1, 0, -92, 180]$$ $$340062928/159201$$ $$40755456$$ $$[2, 2]$$ $$1024$$ $$0.15462$$
3192.i3 3192a1 $$[0, -1, 0, -47, -108]$$ $$733001728/10773$$ $$172368$$ $$$$ $$512$$ $$-0.19195$$ $$\Gamma_0(N)$$-optimal
3192.i4 3192a4 $$[0, -1, 0, 328, 1020]$$ $$3799448348/2736741$$ $$-2802422784$$ $$$$ $$2048$$ $$0.50119$$

## Rank

sage: E.rank()

The elliptic curves in class 3192.i have rank $$0$$.

## Complex multiplication

The elliptic curves in class 3192.i do not have complex multiplication.

## Modular form3192.2.a.i

sage: E.q_eigenform(10)

$$q - q^{3} + 2 q^{5} - q^{7} + q^{9} + 4 q^{11} - 6 q^{13} - 2 q^{15} + 6 q^{17} + q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 