# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("e1")

sage: E.isogeny_class()

## Elliptic curves in class 5070.e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5070.e1 5070e2 $$[1, 1, 0, -7777, -239741]$$ $$10779215329/1232010$$ $$5946676956090$$ $$$$ $$16128$$ $$1.1834$$
5070.e2 5070e1 $$[1, 1, 0, 673, -18351]$$ $$6967871/35100$$ $$-169420995900$$ $$$$ $$8064$$ $$0.83686$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form5070.2.a.e

sage: E.q_eigenform(10)

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