# Properties

 Label 176610.de Number of curves $4$ Conductor $176610$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("de1")

sage: E.isogeny_class()

## Elliptic curves in class 176610.de

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
176610.de1 176610q3 [1, 0, 0, -314131, 67740155] [2] 1433600
176610.de2 176610q2 [1, 0, 0, -19781, 1040445] [2, 2] 716800
176610.de3 176610q1 [1, 0, 0, -2961, -39399] [2] 358400 $$\Gamma_0(N)$$-optimal
176610.de4 176610q4 [1, 0, 0, 5449, 3518031] [2] 1433600

## Rank

sage: E.rank()

The elliptic curves in class 176610.de have rank $$1$$.

## Complex multiplication

The elliptic curves in class 176610.de do not have complex multiplication.

## Modular form 176610.2.a.de

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} - q^{7} + q^{8} + q^{9} - q^{10} + 4q^{11} + q^{12} - 2q^{13} - q^{14} - q^{15} + q^{16} + 6q^{17} + q^{18} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.