# Properties

 Label 33600fe Number of curves $2$ Conductor $33600$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 33600fe

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
33600.du2 33600fe1 $$[0, -1, 0, 39167, 229537]$$ $$2595575/1512$$ $$-3870720000000000$$ $$[]$$ $$207360$$ $$1.6805$$ $$\Gamma_0(N)$$-optimal
33600.du1 33600fe2 $$[0, -1, 0, -560833, 171229537]$$ $$-7620530425/526848$$ $$-1348730880000000000$$ $$[]$$ $$622080$$ $$2.2298$$

## Rank

sage: E.rank()

The elliptic curves in class 33600fe have rank $$1$$.

## Complex multiplication

The elliptic curves in class 33600fe do not have complex multiplication.

## Modular form 33600.2.a.fe

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 