# Properties

 Label 3192.n Number of curves $2$ Conductor $3192$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
E = EllipticCurve("n1")

E.isogeny_class()

## Elliptic curves in class 3192.n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3192.n1 3192f2 $$[0, 1, 0, -168, -864]$$ $$515150500/22743$$ $$23288832$$ $$$$ $$768$$ $$0.17662$$
3192.n2 3192f1 $$[0, 1, 0, -28, 32]$$ $$9826000/2793$$ $$715008$$ $$$$ $$384$$ $$-0.16995$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form3192.2.a.n

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 