Cremona's table of elliptic curves

2730 = 2 · 3 · 5 · 7 · 13

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 7+ 13+	Signs for the Atkin-Lehner involutions
Class	2730k	Isogeny class
Conductor	2730	Conductor
∏ cp	256	Product of Tamagawa factors cp
Δ	8.911747415025E+24	Discriminant
Eigenvalues	2+ 3- 5+ 7+ -4 13+ -2  8	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-139893664,620442907886]	[a1,a2,a3,a4,a6]
j	302773487204995438715379645049/8911747415025000000000000	j-invariant
L	1.165913482582	L(r)(E,1)/r!
Ω	0.072869592661376	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	21840bh2 87360z2 8190bm2 13650bz2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2730k2

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
+	-	+	+	-4	+	-2	8	-4	-2	4	2	6	-8	8	6	0	6	4	8	6	-8	12	-2	-2

---

Quadratic twists for elliptic curve 2730k2

-4	8	-3	5	-7	13
21840bh2	87360z2	8190bm2	13650bz2	19110p2	35490du2

---

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
Back to Tables and computations