# Properties

 Label 92736dz Number of curves $6$ Conductor $92736$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("92736.bh1")

sage: E.isogeny_class()

## Elliptic curves in class 92736dz

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
92736.bh5 92736dz1 [0, 0, 0, 72564, 15409424] [2] 786432 $$\Gamma_0(N)$$-optimal
92736.bh4 92736dz2 [0, 0, 0, -664716, 178495760] [2, 2] 1572864
92736.bh3 92736dz3 [0, 0, 0, -2922636, -1749767920] [2, 2] 3145728
92736.bh2 92736dz4 [0, 0, 0, -10203276, 12544284944] [2] 3145728
92736.bh6 92736dz5 [0, 0, 0, 3609204, -8461886704] [2] 6291456
92736.bh1 92736dz6 [0, 0, 0, -45581196, -118446524656] [2] 6291456

## Rank

sage: E.rank()

The elliptic curves in class 92736dz have rank $$1$$.

## Modular form 92736.2.a.bh

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.