# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("v1")

sage: E.isogeny_class()

## Elliptic curves in class 5070.v

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5070.v1 5070u1 $$[1, 0, 0, -143400, 20940750]$$ $$-2365581049/6750$$ $$-930544819980750$$ $$[]$$ $$39312$$ $$1.7439$$ $$\Gamma_0(N)$$-optimal
5070.v2 5070u2 $$[1, 0, 0, 285015, 107394897]$$ $$18573478391/46875000$$ $$-6462116805421875000$$ $$[]$$ $$117936$$ $$2.2932$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form5070.2.a.v

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 