# Properties

 Label 5070.j Number of curves $2$ Conductor $5070$ CM no Rank $0$ Graph # Learn more

Show commands for: SageMath
sage: E = EllipticCurve("j1")

sage: E.isogeny_class()

## Elliptic curves in class 5070.j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5070.j1 5070i1 $$[1, 0, 1, -849, 9466]$$ $$-2365581049/6750$$ $$-192786750$$ $$$$ $$3024$$ $$0.46139$$ $$\Gamma_0(N)$$-optimal
5070.j2 5070i2 $$[1, 0, 1, 1686, 49012]$$ $$18573478391/46875000$$ $$-1338796875000$$ $$[]$$ $$9072$$ $$1.0107$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form5070.2.a.j

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. 