# Properties

 Label 39600.dv Number of curves 4 Conductor 39600 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("39600.dv1")

sage: E.isogeny_class()

## Elliptic curves in class 39600.dv

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
39600.dv1 39600df3 [0, 0, 0, -289875, -59840750]  331776
39600.dv2 39600df4 [0, 0, 0, -145875, -119312750]  663552
39600.dv3 39600df1 [0, 0, 0, -19875, 1017250]  110592 $$\Gamma_0(N)$$-optimal
39600.dv4 39600df2 [0, 0, 0, 16125, 4293250]  221184

## Rank

sage: E.rank()

The elliptic curves in class 39600.dv have rank $$1$$.

## Modular form 39600.2.a.dv

sage: E.q_eigenform(10)

$$q + 2q^{7} - q^{11} + 4q^{13} - 6q^{17} + 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 