# Properties

 Label 19600.u Number of curves 2 Conductor 19600 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("19600.u1")

sage: E.isogeny_class()

## Elliptic curves in class 19600.u

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
19600.u1 19600w2 [0, 1, 0, -49408, -4192812] [2] 61440
19600.u2 19600w1 [0, 1, 0, -408, -174812] [2] 30720 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 19600.u have rank $$0$$.

## Modular form 19600.2.a.u

sage: E.q_eigenform(10)

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

## 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.