Cremona's table of elliptic curves

7616 = 2⁶ · 7 · 17

Field	Data	Notes
Atkin-Lehner	2- 7+ 17+	Signs for the Atkin-Lehner involutions
Class	7616g	Isogeny class
Conductor	7616	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	22737354752 = 215 · 74 · 172	Discriminant
Eigenvalues	2- -2  0 7+ -6 -6 17+  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1153,12831]	[a1,a2,a3,a4,a6]
Generators	[-21:168:1] [-5:136:1]	Generators of the group modulo torsion
j	5177717000/693889	j-invariant
L	3.9908005171309	L(r)(E,1)/r!
Ω	1.1586290867249	Real period
R	0.86110398980489	Regulator
r	2	Rank of the group of rational points
S	0.99999999999993	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	7616l2 3808a2 68544du2 53312cc2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 7616g2

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

---

Quadratic twists for elliptic curve 7616g2

-4	8	-3	-7	17
7616l2	3808a2	68544du2	53312cc2	129472df2

---

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