# Properties

 Label 3870.o Number of curves $2$ Conductor $3870$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("o1")

sage: E.isogeny_class()

## Elliptic curves in class 3870.o

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3870.o1 3870r2 $$[1, -1, 1, -2138, 37361]$$ $$1481933914201/53916840$$ $$39305376360$$ $$$$ $$4608$$ $$0.80261$$
3870.o2 3870r1 $$[1, -1, 1, -338, -1519]$$ $$5841725401/1857600$$ $$1354190400$$ $$$$ $$2304$$ $$0.45604$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 3870.o have rank $$1$$.

## Complex multiplication

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

## Modular form3870.2.a.o

sage: E.q_eigenform(10)

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