# Properties

 Label 2550.c Number of curves 6 Conductor 2550 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("2550.c1")

sage: E.isogeny_class()

## Elliptic curves in class 2550.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2550.c1 2550b5 [1, 1, 0, -693600, -222626250]  16384
2550.c2 2550b3 [1, 1, 0, -43350, -3492000] [2, 2] 8192
2550.c3 2550b6 [1, 1, 0, -41100, -3867750]  16384
2550.c4 2550b2 [1, 1, 0, -2850, -49500] [2, 2] 4096
2550.c5 2550b1 [1, 1, 0, -850, 8500]  2048 $$\Gamma_0(N)$$-optimal
2550.c6 2550b4 [1, 1, 0, 5650, -279000]  8192

## Rank

sage: E.rank()

The elliptic curves in class 2550.c have rank $$1$$.

## Modular form2550.2.a.c

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} + q^{4} + q^{6} - q^{8} + q^{9} - 4q^{11} - q^{12} + 2q^{13} + q^{16} - q^{17} - q^{18} + 4q^{19} + O(q^{20})$$

## 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 LMFDB numbering.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 