# Properties

 Label 5070.n Number of curves $2$ Conductor $5070$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("n1")

sage: E.isogeny_class()

## Elliptic curves in class 5070.n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5070.n1 5070m2 $$[1, 1, 1, -144076, -21109171]$$ $$68523370149961/243360$$ $$1174652238240$$ $$$$ $$26880$$ $$1.5343$$
5070.n2 5070m1 $$[1, 1, 1, -8876, -342451]$$ $$-16022066761/998400$$ $$-4819086105600$$ $$$$ $$13440$$ $$1.1877$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 5070.n have rank $$0$$.

## Complex multiplication

The elliptic curves in class 5070.n do not have complex multiplication.

## Modular form5070.2.a.n

sage: E.q_eigenform(10)

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