# Properties

 Label 2550.l Number of curves $8$ Conductor $2550$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("l1")

sage: E.isogeny_class()

## Elliptic curves in class 2550.l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2550.l1 2550h7 [1, 0, 1, -2836751, -1839219352] [2] 49152
2550.l2 2550h4 [1, 0, 1, -544001, 154390148] [2] 12288
2550.l3 2550h5 [1, 0, 1, -180501, -27656852] [2, 2] 24576
2550.l4 2550h3 [1, 0, 1, -36001, 2110148] [2, 2] 12288
2550.l5 2550h2 [1, 0, 1, -34001, 2410148] [2, 2] 6144
2550.l6 2550h1 [1, 0, 1, -2001, 42148] [2] 3072 $$\Gamma_0(N)$$-optimal
2550.l7 2550h6 [1, 0, 1, 76499, 12685148] [2] 24576
2550.l8 2550h8 [1, 0, 1, 163749, -120604352] [2] 49152

## Rank

sage: E.rank()

The elliptic curves in class 2550.l have rank $$0$$.

## Complex multiplication

The elliptic curves in class 2550.l do not have complex multiplication.

## Modular form2550.2.a.l

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.

$$\left(\begin{array}{rrrrrrrr} 1 & 16 & 2 & 4 & 8 & 16 & 8 & 4 \\ 16 & 1 & 8 & 4 & 2 & 4 & 8 & 16 \\ 2 & 8 & 1 & 2 & 4 & 8 & 4 & 2 \\ 4 & 4 & 2 & 1 & 2 & 4 & 2 & 4 \\ 8 & 2 & 4 & 2 & 1 & 2 & 4 & 8 \\ 16 & 4 & 8 & 4 & 2 & 1 & 8 & 16 \\ 8 & 8 & 4 & 2 & 4 & 8 & 1 & 8 \\ 4 & 16 & 2 & 4 & 8 & 16 & 8 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.