# Properties

 Label 139230.dc Number of curves 4 Conductor 139230 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("139230.dc1")

sage: E.isogeny_class()

## Elliptic curves in class 139230.dc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
139230.dc1 139230bc3 [1, -1, 1, -6660113, 6617282721]  3932160
139230.dc2 139230bc4 [1, -1, 1, -810833, -121049823]  3932160
139230.dc3 139230bc2 [1, -1, 1, -417713, 102714081] [2, 2] 1966080
139230.dc4 139230bc1 [1, -1, 1, -2993, 4342497]  983040 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 139230.dc have rank $$1$$.

## Modular form 139230.2.a.dc

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} - q^{5} + q^{7} + q^{8} - q^{10} - q^{13} + q^{14} + q^{16} + q^{17} + 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 