# Properties

 Label 3570t Number of curves $6$ Conductor $3570$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("t1")

sage: E.isogeny_class()

## Elliptic curves in class 3570t

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3570.t5 3570t1 $$[1, 1, 1, 3060, 64557]$$ $$3168685387909439/3563732336640$$ $$-3563732336640$$ $$[4]$$ $$9216$$ $$1.0949$$ $$\Gamma_0(N)$$-optimal
3570.t4 3570t2 $$[1, 1, 1, -17420, 588845]$$ $$584614687782041281/184812061593600$$ $$184812061593600$$ $$[2, 4]$$ $$18432$$ $$1.4415$$
3570.t3 3570t3 $$[1, 1, 1, -109900, -13616083]$$ $$146796951366228945601/5397929064360000$$ $$5397929064360000$$ $$[2, 2]$$ $$36864$$ $$1.7881$$
3570.t2 3570t4 $$[1, 1, 1, -252620, 48757805]$$ $$1782900110862842086081/328139630024640$$ $$328139630024640$$ $$[4]$$ $$36864$$ $$1.7881$$
3570.t1 3570t5 $$[1, 1, 1, -1742580, -886120275]$$ $$585196747116290735872321/836876053125000$$ $$836876053125000$$ $$[2]$$ $$73728$$ $$2.1347$$
3570.t6 3570t6 $$[1, 1, 1, 43100, -48377683]$$ $$8854313460877886399/1016927675429790600$$ $$-1016927675429790600$$ $$[2]$$ $$73728$$ $$2.1347$$

## Rank

sage: E.rank()

The elliptic curves in class 3570t have rank $$0$$.

## Complex multiplication

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

## Modular form3570.2.a.t

sage: E.q_eigenform(10)

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

## 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 Cremona numbering.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.