# Properties

 Label 92736cj Number of curves $2$ Conductor $92736$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("cj1")

sage: E.isogeny_class()

## Elliptic curves in class 92736cj

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92736.dn2 92736cj1 $$[0, 0, 0, 19860, -5067344]$$ $$4533086375/60669952$$ $$-11594208380977152$$ $$[2]$$ $$516096$$ $$1.7632$$ $$\Gamma_0(N)$$-optimal
92736.dn1 92736cj2 $$[0, 0, 0, -348780, -74224208]$$ $$24553362849625/1755162752$$ $$335416825271549952$$ $$[2]$$ $$1032192$$ $$2.1098$$

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 92736cj do not have complex multiplication.

## Modular form 92736.2.a.cj

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.