Properties

 Label 39270bp Number of curves 8 Conductor 39270 CM no Rank 1 Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("39270.br1")
sage: E.isogeny_class()

Elliptic curves in class 39270bp

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
39270.br7 39270bp1 [1, 0, 1, -108475448, 1079289750278] 6 17252352 $$\Gamma_0(N)$$-optimal
39270.br6 39270bp2 [1, 0, 1, -2376073528, 44530097120006] 12 34504704
39270.br8 39270bp3 [1, 0, 1, 948970777, -24855007825942] 2 51757056
39270.br5 39270bp4 [1, 0, 1, -3028263528, 18137793952006] 6 69009408
39270.br3 39270bp5 [1, 0, 1, -38005452808, 2851783142342918] 6 69009408
39270.br4 39270bp6 [1, 0, 1, -9201244903, -294611199823894] 4 103514112
39270.br1 39270bp7 [1, 0, 1, -141721078503, -20534789449019414] 2 207028224
39270.br2 39270bp8 [1, 0, 1, -39084862183, 2681211362365418] 2 207028224

Rank

sage: E.rank()

The elliptic curves in class 39270bp have rank $$1$$.

Modular form 39270.2.a.br

sage: E.q_eigenform(10)
$$q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} + q^{7} - q^{8} + q^{9} - q^{10} + q^{11} + q^{12} + 2q^{13} - q^{14} + q^{15} + q^{16} - q^{17} - q^{18} - 4q^{19} + O(q^{20})$$

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 Cremona numbering.

$$\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with Cremona labels.