# Properties

 Label 6534.b Number of curves $3$ Conductor $6534$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("b1")

sage: E.isogeny_class()

## Elliptic curves in class 6534.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6534.b1 6534g3 $$[1, -1, 0, -3471, 80603]$$ $$-132651/2$$ $$-69739270326$$ $$[]$$ $$8100$$ $$0.88374$$
6534.b2 6534g2 $$[1, -1, 0, -1656, -33984]$$ $$-1167051/512$$ $$-220410533376$$ $$[]$$ $$8100$$ $$0.88374$$
6534.b3 6534g1 $$[1, -1, 0, 159, 501]$$ $$9261/8$$ $$-382657176$$ $$[]$$ $$2700$$ $$0.33444$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 6534.b have rank $$0$$.

## Complex multiplication

The elliptic curves in class 6534.b do not have complex multiplication.

## Modular form6534.2.a.b

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - 3 q^{5} + q^{7} - q^{8} + 3 q^{10} + 4 q^{13} - q^{14} + q^{16} - 2 q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 