# Properties

 Label 3850.s Number of curves $4$ Conductor $3850$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("s1")

sage: E.isogeny_class()

## Elliptic curves in class 3850.s

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3850.s1 3850n3 $$[1, -1, 1, -522730, -145336103]$$ $$1010962818911303721/57392720$$ $$896761250000$$ $$$$ $$24576$$ $$1.7601$$
3850.s2 3850n4 $$[1, -1, 1, -54730, 1175897]$$ $$1160306142246441/634128110000$$ $$9908251718750000$$ $$$$ $$24576$$ $$1.7601$$
3850.s3 3850n2 $$[1, -1, 1, -32730, -2256103]$$ $$248158561089321/1859334400$$ $$29052100000000$$ $$[2, 2]$$ $$12288$$ $$1.4135$$
3850.s4 3850n1 $$[1, -1, 1, -730, -80103]$$ $$-2749884201/176619520$$ $$-2759680000000$$ $$$$ $$6144$$ $$1.0670$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 3850.s have rank $$0$$.

## Complex multiplication

The elliptic curves in class 3850.s do not have complex multiplication.

## Modular form3850.2.a.s

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} - q^{7} + q^{8} - 3q^{9} - q^{11} + 6q^{13} - q^{14} + q^{16} + 2q^{17} - 3q^{18} - 4q^{19} + O(q^{20})$$ ## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 