# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("l1")

sage: E.isogeny_class()

## Elliptic curves in class 7098.l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7098.l1 7098h2 $$[1, 0, 1, -871706, -313330054]$$ $$531373116625/2058$$ $$283712776225242$$ $$[]$$ $$78624$$ $$1.9866$$
7098.l2 7098h1 $$[1, 0, 1, -14876, -73006]$$ $$2640625/1512$$ $$208442039675688$$ $$[]$$ $$26208$$ $$1.4373$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form7098.2.a.l

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. 