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	870a	Isogeny class
Conductor	870	Conductor
∏ cp	48	Product of Tamagawa factors cp
Δ	473062500 = 22 · 32 · 56 · 292	Discriminant
Eigenvalues	2+ 3+ 5-  0  0 -6 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-267,-1431]	[a1,a2,a3,a4,a6]
Generators	[-12:21:1]	Generators of the group modulo torsion
j	2117368939321/473062500	j-invariant
L	1.6315300055282	L(r)(E,1)/r!
Ω	1.1993389648567	Real period
R	0.45345256938353	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	6960bl2 27840bg2 2610k2 4350u2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 870a2

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

---

Quadratic twists for elliptic curve 870a2

-4	8	-3	5	-7	-11	29
6960bl2	27840bg2	2610k2	4350u2	42630bl2	105270bo2	25230z2

---

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