# Properties

 Label 3192.f Number of curves $2$ Conductor $3192$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
E = EllipticCurve("f1")

E.isogeny_class()

## Elliptic curves in class 3192.f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3192.f1 3192e2 $$[0, -1, 0, -708, -7020]$$ $$153531250000/1197$$ $$306432$$ $$$$ $$768$$ $$0.22614$$
3192.f2 3192e1 $$[0, -1, 0, -43, -104]$$ $$-562432000/53067$$ $$-849072$$ $$$$ $$384$$ $$-0.12043$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 3192.f have rank $$1$$.

## Complex multiplication

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

## Modular form3192.2.a.f

sage: E.q_eigenform(10)

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

## 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. 