# Properties

 Label 3570.c Number of curves $2$ Conductor $3570$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("c1")

sage: E.isogeny_class()

## Elliptic curves in class 3570.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3570.c1 3570c2 $$[1, 1, 0, -518, 3132]$$ $$15417797707369/4080067320$$ $$4080067320$$ $$$$ $$2304$$ $$0.55269$$
3570.c2 3570c1 $$[1, 1, 0, 82, 372]$$ $$59822347031/83966400$$ $$-83966400$$ $$$$ $$1152$$ $$0.20612$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 3570.c have rank $$1$$.

## Complex multiplication

The elliptic curves in class 3570.c do not have complex multiplication.

## Modular form3570.2.a.c

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} + q^{7} - q^{8} + q^{9} + q^{10} + 2q^{11} - q^{12} - 2q^{13} - q^{14} + q^{15} + q^{16} + q^{17} - q^{18} - 4q^{19} + O(q^{20})$$ ## 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 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. 