# Properties

 Label 92736co Number of curves $6$ Conductor $92736$ CM no Rank $0$ Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("92736.bk1")

sage: E.isogeny_class()

## Elliptic curves in class 92736co

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
92736.bk5 92736co1 [0, 0, 0, 72564, -15409424] [2] 786432 $$\Gamma_0(N)$$-optimal
92736.bk4 92736co2 [0, 0, 0, -664716, -178495760] [2, 2] 1572864
92736.bk3 92736co3 [0, 0, 0, -2922636, 1749767920] [2, 2] 3145728
92736.bk2 92736co4 [0, 0, 0, -10203276, -12544284944] [2] 3145728
92736.bk6 92736co5 [0, 0, 0, 3609204, 8461886704] [2] 6291456
92736.bk1 92736co6 [0, 0, 0, -45581196, 118446524656] [2] 6291456

## Rank

sage: E.rank()

The elliptic curves in class 92736co have rank $$0$$.

## Modular form 92736.2.a.bk

sage: E.q_eigenform(10)

$$q - 2q^{5} + q^{7} - 4q^{11} + 2q^{13} + 6q^{17} - 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.