# Properties

 Label 3525.k Number of curves $2$ Conductor $3525$ CM no Rank $0$ Graph # Learn more

Show commands: SageMath
sage: E = EllipticCurve("k1")

sage: E.isogeny_class()

## Elliptic curves in class 3525.k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3525.k1 3525j2 $$[1, 0, 1, -3576, -82577]$$ $$323535264625/59643$$ $$931921875$$ $$$$ $$3456$$ $$0.72369$$
3525.k2 3525j1 $$[1, 0, 1, -201, -1577]$$ $$-57066625/34263$$ $$-535359375$$ $$$$ $$1728$$ $$0.37712$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 3525.k have rank $$0$$.

## Complex multiplication

The elliptic curves in class 3525.k do not have complex multiplication.

## Modular form3525.2.a.k

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} - q^{4} + q^{6} - 4q^{7} - 3q^{8} + q^{9} - q^{12} - 6q^{13} - 4q^{14} - q^{16} + 6q^{17} + q^{18} + 2q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 