# Properties

 Label 193600j Number of curves 2 Conductor 193600 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("193600.w1")

sage: E.isogeny_class()

## Elliptic curves in class 193600j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
193600.w2 193600j1 [0, 1, 0, 141167, -31995537] [2] 3072000 $$\Gamma_0(N)$$-optimal
193600.w1 193600j2 [0, 1, 0, -1068833, -342965537] [2] 6144000

## Rank

sage: E.rank()

The elliptic curves in class 193600j have rank $$0$$.

## Modular form 193600.2.a.w

sage: E.q_eigenform(10)

$$q - 2q^{3} - 4q^{7} + q^{9} + 6q^{13} + 2q^{17} - 4q^{19} + O(q^{20})$$

## 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.