# Properties

 Label 19600co Number of curves 4 Conductor 19600 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("19600.dm1")

sage: E.isogeny_class()

## Elliptic curves in class 19600co

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
19600.dm3 19600co1 [0, -1, 0, -1633, 18012] [2] 17280 $$\Gamma_0(N)$$-optimal
19600.dm4 19600co2 [0, -1, 0, 4492, 116012] [2] 34560
19600.dm1 19600co3 [0, -1, 0, -50633, -4367488] [2] 51840
19600.dm2 19600co4 [0, -1, 0, -44508, -5469988] [2] 103680

## Rank

sage: E.rank()

The elliptic curves in class 19600co have rank $$1$$.

## Modular form 19600.2.a.dm

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.