# Properties

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

Show commands: SageMath
E = EllipticCurve("j1")

E.isogeny_class()

## Elliptic curves in class 3192.j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3192.j1 3192l1 $$[0, -1, 0, -152, 732]$$ $$381775972/25137$$ $$25740288$$ $$$$ $$1152$$ $$0.17157$$ $$\Gamma_0(N)$$-optimal
3192.j2 3192l2 $$[0, -1, 0, 128, 2860]$$ $$112363774/1842183$$ $$-3772790784$$ $$$$ $$2304$$ $$0.51814$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form3192.2.a.j

sage: E.q_eigenform(10)

$$q - q^{3} + 2 q^{5} - q^{7} + q^{9} + 6 q^{11} - 2 q^{13} - 2 q^{15} - 8 q^{17} + q^{19} + O(q^{20})$$

## 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. 