# Properties

 Label 4290.bb Number of curves 8 Conductor 4290 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("4290.bb1")
sage: E.isogeny_class()

## Elliptic curves in class 4290.bb

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
4290.bb1 4290bb7 [1, 0, 0, -1047000, -231922620] 4 165888
4290.bb2 4290bb6 [1, 0, 0, -913900, -336246400] 4 82944
4290.bb3 4290bb3 [1, 0, 0, -913820, -336308208] 2 41472
4290.bb4 4290bb8 [1, 0, 0, -782080, -436614148] 2 165888
4290.bb5 4290bb4 [1, 0, 0, -471900, 124722000] 12 55296
4290.bb6 4290bb2 [1, 0, 0, -31900, 1610000] 12 27648
4290.bb7 4290bb1 [1, 0, 0, -11420, -450288] 6 13824 $$\Gamma_0(N)$$-optimal
4290.bb8 4290bb5 [1, 0, 0, 80420, 10438352] 6 55296

## Rank

sage: E.rank()

The elliptic curves in class 4290.bb have rank $$1$$.

## Modular form4290.2.a.bb

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

## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.