# Properties

 Label 9792.k Number of curves 6 Conductor 9792 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("9792.k1")

sage: E.isogeny_class()

## Elliptic curves in class 9792.k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
9792.k1 9792k5 [0, 0, 0, -15980556, 24588721136] [2] 196608
9792.k2 9792k3 [0, 0, 0, -998796, 384189680] [2, 2] 98304
9792.k3 9792k6 [0, 0, 0, -946956, 425848304] [2] 196608
9792.k4 9792k2 [0, 0, 0, -65676, 5342960] [2, 2] 49152
9792.k5 9792k1 [0, 0, 0, -19596, -979216] [2] 24576 $$\Gamma_0(N)$$-optimal
9792.k6 9792k4 [0, 0, 0, 130164, 31115504] [2] 98304

## Rank

sage: E.rank()

The elliptic curves in class 9792.k have rank $$0$$.

## Modular form9792.2.a.k

sage: E.q_eigenform(10)

$$q - 2q^{5} - 4q^{11} + 2q^{13} - q^{17} - 4q^{19} + O(q^{20})$$

## 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.