# Properties

 Label 120666d Number of curves $6$ Conductor $120666$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("120666.o1")

sage: E.isogeny_class()

## Elliptic curves in class 120666d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
120666.o5 120666d1 [1, 1, 0, -11871239, 15718529013] [2] 8847360 $$\Gamma_0(N)$$-optimal
120666.o4 120666d2 [1, 1, 0, -15332359, 5801035765] [2, 2] 17694720
120666.o6 120666d3 [1, 1, 0, 59135801, 45701075893] [2] 35389440
120666.o2 120666d4 [1, 1, 0, -145178439, -668749349835] [2, 2] 35389440
120666.o3 120666d5 [1, 1, 0, -49450079, -1537369342803] [2] 70778880
120666.o1 120666d6 [1, 1, 0, -2318444079, -42968757113667] [2] 70778880

## Rank

sage: E.rank()

The elliptic curves in class 120666d have rank $$0$$.

## Modular form 120666.2.a.o

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} + q^{4} + 2q^{5} + q^{6} - q^{7} - q^{8} + q^{9} - 2q^{10} - 4q^{11} - q^{12} + q^{14} - 2q^{15} + q^{16} + q^{17} - q^{18} - 4q^{19} + O(q^{20})$$

## 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 Cremona 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 Cremona labels.