# Properties

 Label 82810.q Number of curves $4$ Conductor $82810$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("82810.q1")

sage: E.isogeny_class()

## Elliptic curves in class 82810.q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
82810.q1 82810e4 [1, -1, 0, -2216720, 1270815846] [2] 1474560
82810.q2 82810e3 [1, -1, 0, -726140, -222380950] [2] 1474560
82810.q3 82810e2 [1, -1, 0, -146470, 17486496] [2, 2] 737280
82810.q4 82810e1 [1, -1, 0, 19150, 1620100] [2] 368640 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 82810.q have rank $$0$$.

## Modular form 82810.2.a.q

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - q^{5} - q^{8} - 3q^{9} + q^{10} - 4q^{11} + q^{16} - 2q^{17} + 3q^{18} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.