Cremona's table of elliptic curves

870 = 2 · 3 · 5 · 29

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 29-	Signs for the Atkin-Lehner involutions
Class	870b	Isogeny class
Conductor	870	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	35030827008000 = 230 · 32 · 53 · 29	Discriminant
Eigenvalues	2+ 3- 5+  2 -6 -4 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-32844,-2275958]	[a1,a2,a3,a4,a6]
Generators	[-778:595:8]	Generators of the group modulo torsion
j	3918075806073018169/35030827008000	j-invariant
L	1.9885607214778	L(r)(E,1)/r!
Ω	0.35483090158862	Real period
R	5.6042489889543	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	6960w3 27840w3 2610m3 4350s3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 870b3

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
+	-	+	2	-6	-4	-6	-4	0	-	2	2	0	-4	0	6	-12	-4	8	0	2	-10	18	0	-10

---

Quadratic twists for elliptic curve 870b3

-4	8	-3	5	-7	-11	29
6960w3	27840w3	2610m3	4350s3	42630bb3	105270bt3	25230o3

---

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