# Properties

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

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

sage: E.isogeny_class()

## Elliptic curves in class 6534.bc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6534.bc1 6534ba3 [1, -1, 1, -14906, 932473] [] 24300
6534.bc2 6534ba1 [1, -1, 1, -386, -2857] [] 2700 $$\Gamma_0(N)$$-optimal
6534.bc3 6534ba2 [1, -1, 1, 1429, -14957] [] 8100

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form6534.2.a.bc

sage: E.q_eigenform(10)

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

## 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. 