# Properties

 Label 5775.v Number of curves $6$ Conductor $5775$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("5775.v1")

sage: E.isogeny_class()

## Elliptic curves in class 5775.v

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
5775.v1 5775u5 [1, 0, 1, -331251, -73404977] [2] 49152
5775.v2 5775u3 [1, 0, 1, -21876, -1011227] [2, 2] 24576
5775.v3 5775u2 [1, 0, 1, -6751, 198773] [2, 2] 12288
5775.v4 5775u1 [1, 0, 1, -6626, 207023] [2] 6144 $$\Gamma_0(N)$$-optimal
5775.v5 5775u4 [1, 0, 1, 6374, 881273] [2] 24576
5775.v6 5775u6 [1, 0, 1, 45499, -5996977] [2] 49152

## Rank

sage: E.rank()

The elliptic curves in class 5775.v have rank $$0$$.

## Modular form5775.2.a.v

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} - q^{4} + q^{6} + q^{7} - 3q^{8} + q^{9} + q^{11} - q^{12} + 2q^{13} + q^{14} - q^{16} + 6q^{17} + q^{18} - 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.