# Properties

 Label 62790bt Number of curves 8 Conductor 62790 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("62790.bu1")

sage: E.isogeny_class()

## Elliptic curves in class 62790bt

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
62790.bu7 62790bt1 [1, 0, 0, -167843570, 843125287812] [12] 19021824 $$\Gamma_0(N)$$-optimal
62790.bu6 62790bt2 [1, 0, 0, -2691000050, 53729999002500] [2, 6] 38043648
62790.bu8 62790bt3 [1, 0, 0, 513852430, 4463105748612] [4] 57065472
62790.bu5 62790bt4 [1, 0, 0, -2696503730, 53499182368452] [6] 76087296
62790.bu2 62790bt5 [1, 0, 0, -43056000050, 3438730826002500] [6] 76087296
62790.bu4 62790bt6 [1, 0, 0, -2961450050, 42276481912500] [2, 2] 114130944
62790.bu3 62790bt7 [1, 0, 0, -18469941230, -933806241069048] [2] 228261888
62790.bu1 62790bt8 [1, 0, 0, -43057798550, 3438429180592800] [2] 228261888

## Rank

sage: E.rank()

The elliptic curves in class 62790bt have rank $$0$$.

## Modular form 62790.2.a.bu

sage: E.q_eigenform(10)

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

## 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.