# Properties

 Label 151725.bg Number of curves 4 Conductor 151725 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("151725.bg1")

sage: E.isogeny_class()

## Elliptic curves in class 151725.bg

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
151725.bg1 151725t4 [1, 0, 0, -812963, -282180708]  1966080
151725.bg2 151725t2 [1, 0, 0, -54338, -3765333] [2, 2] 983040
151725.bg3 151725t1 [1, 0, 0, -18213, 894792]  491520 $$\Gamma_0(N)$$-optimal
151725.bg4 151725t3 [1, 0, 0, 126287, -23453458]  1966080

## Rank

sage: E.rank()

The elliptic curves in class 151725.bg have rank $$1$$.

## Modular form 151725.2.a.bg

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 