# Properties

 Label 3549.a Number of curves $2$ Conductor $3549$ CM no Rank $1$ Graph # Learn more

Show commands: SageMath
sage: E = EllipticCurve("a1")

sage: E.isogeny_class()

## Elliptic curves in class 3549.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3549.a1 3549b2 $$[0, 1, 1, -64302, 6254642]$$ $$-13383627864961024/151263$$ $$-332324811$$ $$[]$$ $$12000$$ $$1.2032$$
3549.a2 3549b1 $$[0, 1, 1, 48, 1460]$$ $$5451776/413343$$ $$-908114571$$ $$[]$$ $$2400$$ $$0.39844$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 3549.a have rank $$1$$.

## Complex multiplication

The elliptic curves in class 3549.a do not have complex multiplication.

## Modular form3549.2.a.a

sage: E.q_eigenform(10)

$$q - 2q^{2} + q^{3} + 2q^{4} - 3q^{5} - 2q^{6} - q^{7} + q^{9} + 6q^{10} + 2q^{12} + 2q^{14} - 3q^{15} - 4q^{16} + 2q^{17} - 2q^{18} - q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 