# Properties

 Label 92736fj Number of curves $2$ Conductor $92736$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("fj1")

sage: E.isogeny_class()

## Elliptic curves in class 92736fj

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92736.da2 92736fj1 $$[0, 0, 0, -1020, 16112]$$ $$-9826000/3703$$ $$-44228395008$$ $$$$ $$61440$$ $$0.75255$$ $$\Gamma_0(N)$$-optimal
92736.da1 92736fj2 $$[0, 0, 0, -17580, 897104]$$ $$12576878500/1127$$ $$53843263488$$ $$$$ $$122880$$ $$1.0991$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 92736.2.a.fj

sage: E.q_eigenform(10)

$$q + q^{7} - 4q^{11} - 6q^{13} + O(q^{20})$$ ## 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. 