# Properties

 Label 19600.cj Number of curves $4$ Conductor $19600$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("cj1")

sage: E.isogeny_class()

## Elliptic curves in class 19600.cj

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
19600.cj1 19600h4 $$[0, 0, 0, -366275, 85321250]$$ $$1443468546/7$$ $$26353376000000$$ $$[2]$$ $$98304$$ $$1.7756$$
19600.cj2 19600h3 $$[0, 0, 0, -72275, -5916750]$$ $$11090466/2401$$ $$9039207968000000$$ $$[2]$$ $$98304$$ $$1.7756$$
19600.cj3 19600h2 $$[0, 0, 0, -23275, 1286250]$$ $$740772/49$$ $$92236816000000$$ $$[2, 2]$$ $$49152$$ $$1.4291$$
19600.cj4 19600h1 $$[0, 0, 0, 1225, 85750]$$ $$432/7$$ $$-3294172000000$$ $$[2]$$ $$24576$$ $$1.0825$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 19600.2.a.cj

sage: E.q_eigenform(10)

$$q - 3q^{9} + 4q^{11} + 2q^{13} - 6q^{17} + 8q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.