Cremona's table of elliptic curves

3705 = 3 · 5 · 13 · 19

Field	Data	Notes
Atkin-Lehner	3+ 5- 13+ 19-	Signs for the Atkin-Lehner involutions
Class	3705c	Isogeny class
Conductor	3705	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	187909245225 = 36 · 52 · 134 · 192	Discriminant
Eigenvalues	-1 3+ 5- -4  0 13+  2 19-	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-1450,-4690]	[a1,a2,a3,a4,a6]
Generators	[-10:99:1]	Generators of the group modulo torsion
j	337168068688801/187909245225	j-invariant
L	1.7047708279366	L(r)(E,1)/r!
Ω	0.83020586025696	Real period
R	2.0534314554332	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	59280bv2 11115d2 18525o2 48165c2	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 3705c2

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
-1	+	-	-4	0	+	2	-	-8	2	8	2	-2	0	0	6	-4	14	-12	-8	10	-8	12	14	6

---

Quadratic twists for elliptic curve 3705c2

-4	-3	5	13	-19
59280bv2	11115d2	18525o2	48165c2	70395s2

---

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