# Properties

 Label 7098.bc Number of curves $4$ Conductor $7098$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("bc1")

sage: E.isogeny_class()

## Elliptic curves in class 7098.bc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7098.bc1 7098y3 $$[1, 0, 0, -13517, 603537]$$ $$124318741396429/51631104$$ $$113433535488$$ $$$$ $$12000$$ $$1.0830$$
7098.bc2 7098y4 $$[1, 0, 0, -11437, 796145]$$ $$-75306487574989/81352871712$$ $$-178732259151264$$ $$$$ $$24000$$ $$1.4296$$
7098.bc3 7098y1 $$[1, 0, 0, -452, -3732]$$ $$4649101309/6804$$ $$14948388$$ $$$$ $$2400$$ $$0.27833$$ $$\Gamma_0(N)$$-optimal
7098.bc4 7098y2 $$[1, 0, 0, -322, -5890]$$ $$-1680914269/5786802$$ $$-12713603994$$ $$$$ $$4800$$ $$0.62490$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form7098.2.a.bc

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 