Properties

 Label 364560ek Number of curves $6$ Conductor $364560$ CM no Rank $0$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("364560.ek1")

sage: E.isogeny_class()

Elliptic curves in class 364560ek

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
364560.ek6 364560ek1 [0, 1, 0, 47024, -22221676] [2] 4718592 $$\Gamma_0(N)$$-optimal
364560.ek5 364560ek2 [0, 1, 0, -956496, -340538220] [2, 2] 9437184
364560.ek4 364560ek3 [0, 1, 0, -2900816, 1481678484] [2] 18874368
364560.ek2 364560ek4 [0, 1, 0, -15068496, -22518957420] [2, 2] 18874368
364560.ek3 364560ek5 [0, 1, 0, -14833296, -23255697900] [2] 37748736
364560.ek1 364560ek6 [0, 1, 0, -241095696, -1440975253740] [2] 37748736

Rank

sage: E.rank()

The elliptic curves in class 364560ek have rank $$0$$.

Modular form 364560.2.a.ek

sage: E.q_eigenform(10)

$$q + q^{3} - q^{5} + q^{9} + 4q^{11} - 6q^{13} - q^{15} - 2q^{17} + 4q^{19} + O(q^{20})$$

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.