# Properties

 Label 52983a Number of curves 6 Conductor 52983 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("52983.e1")
sage: E.isogeny_class()

## Elliptic curves in class 52983a

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
52983.e6 52983a1 [1, -1, 1, 7411, 52260] 2 100352 $$\Gamma_0(N)$$-optimal
52983.e5 52983a2 [1, -1, 1, -30434, 445848] 4 200704
52983.e3 52983a3 [1, -1, 1, -295349, -61332330] 2 401408
52983.e2 52983a4 [1, -1, 1, -371039, 86959518] 4 401408
52983.e4 52983a5 [1, -1, 1, -257504, 141093006] 2 802816
52983.e1 52983a6 [1, -1, 1, -5934254, 5565613650] 2 802816

## Rank

sage: E.rank()

The elliptic curves in class 52983a have rank $$0$$.

## Modular form 52983.2.a.e

sage: E.q_eigenform(10)
$$q - q^{2} - q^{4} + 2q^{5} - q^{7} + 3q^{8} - 2q^{10} + 4q^{11} - 2q^{13} + q^{14} - q^{16} - 6q^{17} - 4q^{19} + O(q^{20})$$

## 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 Cremona 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 Cremona labels.