# Properties

 Label 19600.n Number of curves $2$ Conductor $19600$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("n1")

sage: E.isogeny_class()

## Elliptic curves in class 19600.n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
19600.n1 19600z2 $$[0, 1, 0, -294408, 43631188]$$ $$2185454/625$$ $$807072140000000000$$ $$$$ $$258048$$ $$2.1426$$
19600.n2 19600z1 $$[0, 1, 0, 48592, 4529188]$$ $$19652/25$$ $$-16141442800000000$$ $$$$ $$129024$$ $$1.7960$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 19600.2.a.n

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 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. 