# Properties

 Label 53067q Number of curves 6 Conductor 53067 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("53067.r1")

sage: E.isogeny_class()

## Elliptic curves in class 53067q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
53067.r6 53067q1 [1, 0, 1, 17320, -191887] [2] 165888 $$\Gamma_0(N)$$-optimal
53067.r5 53067q2 [1, 0, 1, -71125, -1571629] [2, 2] 331776
53067.r3 53067q3 [1, 0, 1, -690240, 219328603] [2] 663552
53067.r2 53067q4 [1, 0, 1, -867130, -310421569] [2, 2] 663552
53067.r4 53067q5 [1, 0, 1, -601795, -503903851] [2] 1327104
53067.r1 53067q6 [1, 0, 1, -13868545, -19880151427] [2] 1327104

## Rank

sage: E.rank()

The elliptic curves in class 53067q have rank $$0$$.

## Modular form 53067.2.a.r

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} - q^{4} + 2q^{5} + q^{6} - 3q^{8} + q^{9} + 2q^{10} + 4q^{11} - q^{12} - 2q^{13} + 2q^{15} - q^{16} + 6q^{17} + q^{18} + O(q^{20})$$

## 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.