# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("bb1")

sage: E.isogeny_class()

## Elliptic curves in class 7098.bb

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7098.bb1 7098ba2 $$[1, 0, 0, -5158, -143014]$$ $$531373116625/2058$$ $$58778538$$ $$[]$$ $$6048$$ $$0.70410$$
7098.bb2 7098ba1 $$[1, 0, 0, -88, -40]$$ $$2640625/1512$$ $$43184232$$ $$$$ $$2016$$ $$0.15479$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form7098.2.a.bb

sage: E.q_eigenform(10)

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