# Properties

 Label 84966.dr Number of curves 6 Conductor 84966 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("84966.dr1")

sage: E.isogeny_class()

## Elliptic curves in class 84966.dr

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
84966.dr1 84966dv6 [1, 0, 0, -392883079, 2997356200775] [2] 14155776
84966.dr2 84966dv4 [1, 0, 0, -24555469, 46831048109] [2, 2] 7077888
84966.dr3 84966dv5 [1, 0, 0, -23280979, 51909380963] [2] 14155776
84966.dr4 84966dv2 [1, 0, 0, -1614649, 651177449] [2, 2] 3538944
84966.dr5 84966dv1 [1, 0, 0, -481769, -119407527] [2] 1769472 $$\Gamma_0(N)$$-optimal
84966.dr6 84966dv3 [1, 0, 0, 3200091, 3793276773] [2] 7077888

## Rank

sage: E.rank()

The elliptic curves in class 84966.dr have rank $$0$$.

## Modular form 84966.2.a.dr

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} - 2q^{5} + q^{6} + q^{8} + q^{9} - 2q^{10} + 4q^{11} + q^{12} + 2q^{13} - 2q^{15} + q^{16} + q^{18} - 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.