# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("139230.dl1")

sage: E.isogeny_class()

## Elliptic curves in class 139230bh

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
139230.dl4 139230bh1 [1, -1, 1, -48848, 38067]  884736 $$\Gamma_0(N)$$-optimal
139230.dl2 139230bh2 [1, -1, 1, -535568, -150261069] [2, 2] 1769472
139230.dl3 139230bh3 [1, -1, 1, -296888, -285067533]  3538944
139230.dl1 139230bh4 [1, -1, 1, -8561768, -9640439949]  3538944

## Rank

sage: E.rank()

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

## Modular form 139230.2.a.dl

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} - q^{5} + q^{7} + q^{8} - q^{10} + 4q^{11} + q^{13} + q^{14} + q^{16} - q^{17} - 4q^{19} + O(q^{20})$$

## 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 Cremona numbering.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 