# Properties

 Label 3870y Number of curves $4$ Conductor $3870$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("y1")

sage: E.isogeny_class()

## Elliptic curves in class 3870y

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3870.z3 3870y1 [1, -1, 1, -617, 6041] [4] 1536 $$\Gamma_0(N)$$-optimal
3870.z2 3870y2 [1, -1, 1, -797, 2369] [2, 2] 3072
3870.z1 3870y3 [1, -1, 1, -7547, -248731] [2] 6144
3870.z4 3870y4 [1, -1, 1, 3073, 16301] [2] 6144

## Rank

sage: E.rank()

The elliptic curves in class 3870y have rank $$0$$.

## Complex multiplication

The elliptic curves in class 3870y do not have complex multiplication.

## Modular form3870.2.a.y

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + q^{5} + 4q^{7} + q^{8} + q^{10} - 2q^{13} + 4q^{14} + q^{16} - 2q^{17} + 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.