# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("dt1")

sage: E.isogeny_class()

## Elliptic curves in class 92736dt

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
92736.cj2 92736dt1 $$[0, 0, 0, 19860, 5067344]$$ $$4533086375/60669952$$ $$-11594208380977152$$ $$$$ $$516096$$ $$1.7632$$ $$\Gamma_0(N)$$-optimal
92736.cj1 92736dt2 $$[0, 0, 0, -348780, 74224208]$$ $$24553362849625/1755162752$$ $$335416825271549952$$ $$$$ $$1032192$$ $$2.1098$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 92736.2.a.dt

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. 