# Properties

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

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 19600u

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
19600.de2 19600u1 $$[0, -1, 0, 992, -13488]$$ $$19652/25$$ $$-137200000000$$ $$[2]$$ $$18432$$ $$0.82304$$ $$\Gamma_0(N)$$-optimal
19600.de1 19600u2 $$[0, -1, 0, -6008, -125488]$$ $$2185454/625$$ $$6860000000000$$ $$[2]$$ $$36864$$ $$1.1696$$

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 19600u do not have complex multiplication.

## Modular form 19600.2.a.u

sage: E.q_eigenform(10)

$$q + 2 q^{3} + q^{9} - 4 q^{11} - 2 q^{13} - 2 q^{19} + O(q^{20})$$

## 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.