# Properties

 Label 369600.fj Number of curves $4$ Conductor $369600$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("fj1")

sage: E.isogeny_class()

## Elliptic curves in class 369600.fj

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
369600.fj1 369600fj4 $$[0, -1, 0, -2957633, -1956796863]$$ $$1397097631688978/433125$$ $$887040000000000$$ $$$$ $$6291456$$ $$2.2307$$
369600.fj2 369600fj2 $$[0, -1, 0, -185633, -30256863]$$ $$690862540036/12006225$$ $$12294374400000000$$ $$[2, 2]$$ $$3145728$$ $$1.8841$$
369600.fj3 369600fj1 $$[0, -1, 0, -23633, 685137]$$ $$5702413264/2525985$$ $$646652160000000$$ $$$$ $$1572864$$ $$1.5376$$ $$\Gamma_0(N)$$-optimal
369600.fj4 369600fj3 $$[0, -1, 0, -5633, -86596863]$$ $$-9653618/1581886845$$ $$-3239704258560000000$$ $$$$ $$6291456$$ $$2.2307$$

## Rank

sage: E.rank()

The elliptic curves in class 369600.fj have rank $$0$$.

## Complex multiplication

The elliptic curves in class 369600.fj do not have complex multiplication.

## Modular form 369600.2.a.fj

sage: E.q_eigenform(10)

$$q - q^{3} - q^{7} + q^{9} + q^{11} + 2 q^{13} + 6 q^{17} - 4 q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 