Properties

 Label 146523s Number of curves $6$ Conductor $146523$ CM no Rank $0$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("146523.y1")

sage: E.isogeny_class()

Elliptic curves in class 146523s

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
146523.y4 146523s1 [1, 0, 1, -26326317, 51989348491] [2] 6193152 $$\Gamma_0(N)$$-optimal
146523.y3 146523s2 [1, 0, 1, -26570522, 50975604695] [2, 2] 12386304
146523.y5 146523s3 [1, 0, 1, 10792843, 182957955221] [2] 24772608
146523.y2 146523s4 [1, 0, 1, -67841167, -145885371955] [2, 2] 24772608
146523.y6 146523s5 [1, 0, 1, 189306698, -987890341111] [2] 49545216
146523.y1 146523s6 [1, 0, 1, -985319352, -11902817825819] [2] 49545216

Rank

sage: E.rank()

The elliptic curves in class 146523s have rank $$0$$.

Modular form 146523.2.a.y

sage: E.q_eigenform(10)

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

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 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.