# Properties

 Label 96192y Number of curves 2 Conductor 96192 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("96192.x1")

sage: E.isogeny_class()

## Elliptic curves in class 96192y

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
96192.x2 96192y1 [0, 0, 0, -2604, -212528]  221184 $$\Gamma_0(N)$$-optimal
96192.x1 96192y2 [0, 0, 0, -71724, -7373360]  442368

## Rank

sage: E.rank()

The elliptic curves in class 96192y have rank $$0$$.

## Modular form 96192.2.a.x

sage: E.q_eigenform(10)

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

## 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 Cremona 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 Cremona labels. 