# Properties

 Label 193600w Number of curves 2 Conductor 193600 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("193600.bd1")

sage: E.isogeny_class()

## Elliptic curves in class 193600w

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
193600.bd2 193600w1 [0, 1, 0, -4033, 384063] [] 430080 $$\Gamma_0(N)$$-optimal
193600.bd1 193600w2 [0, 1, 0, -5812033, -5395247937] [] 4730880

## Rank

sage: E.rank()

The elliptic curves in class 193600w have rank $$1$$.

## Modular form 193600.2.a.bd

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 