# Properties

 Label 369600.fe Number of curves $2$ Conductor $369600$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("fe1")

sage: E.isogeny_class()

## Elliptic curves in class 369600.fe

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
369600.fe1 369600fe2 $$[0, -1, 0, -3547633, -2082282863]$$ $$19288565375865424/3837216796875$$ $$982327500000000000000$$ $$[2]$$ $$13271040$$ $$2.7443$$
369600.fe2 369600fe1 $$[0, -1, 0, 461867, -193808363]$$ $$681010157060096/1406657896875$$ $$-22506526350000000000$$ $$[2]$$ $$6635520$$ $$2.3977$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 369600.2.a.fe

sage: E.q_eigenform(10)

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

## 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.