Properties

 Label 177450x Number of curves $6$ Conductor $177450$ CM no Rank $0$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("177450.jl1")

sage: E.isogeny_class()

Elliptic curves in class 177450x

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
177450.jl6 177450x1 [1, 0, 0, 42162, -4659708] [2] 1769472 $$\Gamma_0(N)$$-optimal
177450.jl5 177450x2 [1, 0, 0, -295838, -48261708] [2, 2] 3538944
177450.jl4 177450x3 [1, 0, 0, -1563338, 710970792] [2] 7077888
177450.jl2 177450x4 [1, 0, 0, -4436338, -3596670208] [2, 2] 7077888
177450.jl3 177450x5 [1, 0, 0, -4140588, -4096783458] [2] 14155776
177450.jl1 177450x6 [1, 0, 0, -70980088, -230178138958] [2] 14155776

Rank

sage: E.rank()

The elliptic curves in class 177450x have rank $$0$$.

Modular form 177450.2.a.jl

sage: E.q_eigenform(10)

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

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.