Cremona's table of elliptic curves

3870 = 2 · 3² · 5 · 43

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 43+	Signs for the Atkin-Lehner involutions
Class	3870r	Isogeny class
Conductor	3870	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	39305376360 = 23 · 312 · 5 · 432	Discriminant
Eigenvalues	2- 3- 5+ -2  2 -2  4 -6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-2138,37361]	[a1,a2,a3,a4,a6]
Generators	[51:217:1]	Generators of the group modulo torsion
j	1481933914201/53916840	j-invariant
L	4.781412204364	L(r)(E,1)/r!
Ω	1.1416580217919	Real period
R	0.69802166572601	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	30960bn2 123840de2 1290f2 19350y2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3870r2

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	2	-2	4	-6	-6	10	-8	2	-2	+	2	-10	-2	-12	-12	-16	16	-8	12	-6	6

---

Quadratic twists for elliptic curve 3870r2

-4	8	-3	5
30960bn2	123840de2	1290f2	19350y2

---

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