Properties

 Label 333795.w Number of curves $6$ Conductor $333795$ CM no Rank $1$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("333795.w1")

sage: E.isogeny_class()

Elliptic curves in class 333795.w

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
333795.w1 333795w6 [1, 0, 0, -3829256, -2884343355] [2] 9437184
333795.w2 333795w4 [1, 0, 0, -252881, -39694680] [2, 2] 4718592
333795.w3 333795w2 [1, 0, 0, -78036, 7828191] [2, 2] 2359296
333795.w4 333795w1 [1, 0, 0, -76591, 8152160] [2] 1179648 $$\Gamma_0(N)$$-optimal
333795.w5 333795w3 [1, 0, 0, 73689, 34622826] [2] 4718592
333795.w6 333795w5 [1, 0, 0, 525974, -235810369] [2] 9437184

Rank

sage: E.rank()

The elliptic curves in class 333795.w have rank $$1$$.

Modular form 333795.2.a.w

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} - q^{4} - q^{5} - q^{6} + q^{7} + 3q^{8} + q^{9} + q^{10} - q^{11} - q^{12} - 2q^{13} - q^{14} - q^{15} - q^{16} - q^{18} - 4q^{19} + O(q^{20})$$

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.