# Properties

 Label 3850.k Number of curves 4 Conductor 3850 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("3850.k1")

sage: E.isogeny_class()

## Elliptic curves in class 3850.k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3850.k1 3850d4 [1, 1, 0, -652900, -197575500]  82944
3850.k2 3850d2 [1, 1, 0, -89400, 10160000]  27648
3850.k3 3850d1 [1, 1, 0, -1400, 392000]  13824 $$\Gamma_0(N)$$-optimal
3850.k4 3850d3 [1, 1, 0, 12600, -10570000]  41472

## Rank

sage: E.rank()

The elliptic curves in class 3850.k have rank $$1$$.

## Modular form3850.2.a.k

sage: E.q_eigenform(10)

$$q - q^{2} + 2q^{3} + q^{4} - 2q^{6} - q^{7} - q^{8} + q^{9} - q^{11} + 2q^{12} + 4q^{13} + q^{14} + q^{16} - q^{18} - 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 