Cremona's table of elliptic curves

3978 = 2 · 3² · 13 · 17

Field	Data	Notes
Atkin-Lehner	2- 3- 13+ 17+	Signs for the Atkin-Lehner involutions
Class	3978g	Isogeny class
Conductor	3978	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	887388372 = 22 · 310 · 13 · 172	Discriminant
Eigenvalues	2- 3-  0 -2  2 13+ 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-2525,-48175]	[a1,a2,a3,a4,a6]
Generators	[-29:18:1]	Generators of the group modulo torsion
j	2441288319625/1217268	j-invariant
L	5.0637263914551	L(r)(E,1)/r!
Ω	0.67353573748182	Real period
R	1.8795314449041	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	31824s2 127296v2 1326c2 99450bh2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3978g2

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	-2	2	+	+	-4	-4	2	-2	-8	0	-4	0	6	0	2	4	10	-12	8	-12	6	-16

---

Quadratic twists for elliptic curve 3978g2

-4	8	-3	5	13	17
31824s2	127296v2	1326c2	99450bh2	51714a2	67626t2

---

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