# Properties

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

Show commands: SageMath
E = EllipticCurve("p1")

E.isogeny_class()

## Elliptic curves in class 7098.p

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7098.p1 7098p1 $$[1, 0, 1, -11782, -493192]$$ $$-82318551880501/54432$$ $$-119587104$$ $$[]$$ $$12000$$ $$0.86692$$ $$\Gamma_0(N)$$-optimal
7098.p2 7098p2 $$[1, 0, 1, 24293, -2543578]$$ $$721710134999099/1691848015872$$ $$-3716990090870784$$ $$[]$$ $$60000$$ $$1.6716$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form7098.2.a.p

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 