# Properties

 Label 277970.bb Number of curves 4 Conductor 277970 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("277970.bb1")

sage: E.isogeny_class()

## Elliptic curves in class 277970.bb

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
277970.bb1 277970bb4 [1, 1, 0, -9427883, 10822507073]  23887872
277970.bb2 277970bb2 [1, 1, 0, -1290943, -560081403]  7962624
277970.bb3 277970bb1 [1, 1, 0, -20223, -21550267]  3981312 $$\Gamma_0(N)$$-optimal
277970.bb4 277970bb3 [1, 1, 0, 181937, 580360917]  11943936

## Rank

sage: E.rank()

The elliptic curves in class 277970.bb have rank $$1$$.

## Modular form 277970.2.a.bb

sage: E.q_eigenform(10)

$$q - q^{2} + 2q^{3} + q^{4} - q^{5} - 2q^{6} + q^{7} - q^{8} + q^{9} + q^{10} - q^{11} + 2q^{12} + 4q^{13} - q^{14} - 2q^{15} + q^{16} - q^{18} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 