# Properties

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

Show commands: SageMath
E = EllipticCurve("l1")

E.isogeny_class()

## Elliptic curves in class 3192.l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3192.l1 3192p2 $$[0, 1, 0, -320, -816]$$ $$3550014724/1842183$$ $$1886395392$$ $$$$ $$2304$$ $$0.47179$$
3192.l2 3192p1 $$[0, 1, 0, -180, 864]$$ $$2533446736/25137$$ $$6435072$$ $$$$ $$1152$$ $$0.12521$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form3192.2.a.l

sage: E.q_eigenform(10)

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

## 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. 