# Properties

 Label 3192.k Number of curves $2$ Conductor $3192$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("k1")

E.isogeny_class()

## Elliptic curves in class 3192.k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3192.k1 3192o1 $$[0, 1, 0, -35, -66]$$ $$304900096/96957$$ $$1551312$$ $$[2]$$ $$768$$ $$-0.10828$$ $$\Gamma_0(N)$$-optimal
3192.k2 3192o2 $$[0, 1, 0, 100, -336]$$ $$427694384/477603$$ $$-122266368$$ $$[2]$$ $$1536$$ $$0.23829$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form3192.2.a.k

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.