# Properties

 Label 7098.n Number of curves $2$ Conductor $7098$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 7098.n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7098.n1 7098i2 $$[1, 0, 1, -620989828, -5956328145220]$$ $$-5486773802537974663600129/2635437714$$ $$-12720754476874626$$ $$[]$$ $$1382976$$ $$3.3290$$
7098.n2 7098i1 $$[1, 0, 1, 120662, -182269540]$$ $$40251338884511/2997011332224$$ $$-14466001271480793216$$ $$[]$$ $$197568$$ $$2.3561$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 7098.n have rank $$0$$.

## Complex multiplication

The elliptic curves in class 7098.n do not have complex multiplication.

## Modular form7098.2.a.n

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 