# Properties

 Label 7056.k Number of curves $6$ Conductor $7056$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("7056.k1")

sage: E.isogeny_class()

## Elliptic curves in class 7056.k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7056.k1 7056by3 [0, 0, 0, -9483411, -11240741806] [2] 147456
7056.k2 7056by5 [0, 0, 0, -6449331, 6243532274] [2] 294912
7056.k3 7056by4 [0, 0, 0, -733971, -85657390] [2, 2] 147456
7056.k4 7056by2 [0, 0, 0, -592851, -175550830] [2, 2] 73728
7056.k5 7056by1 [0, 0, 0, -28371, -4061806] [2] 36864 $$\Gamma_0(N)$$-optimal
7056.k6 7056by6 [0, 0, 0, 2723469, -661666894] [2] 294912

## Rank

sage: E.rank()

The elliptic curves in class 7056.k have rank $$0$$.

## Modular form7056.2.a.k

sage: E.q_eigenform(10)

$$q - 2q^{5} - 4q^{11} - 6q^{13} + 2q^{17} - 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.