Cremona's table of elliptic curves

6708 = 2² · 3 · 13 · 43

Field	Data	Notes
Atkin-Lehner	2- 3+ 13+ 43-	Signs for the Atkin-Lehner involutions
Class	6708c	Isogeny class
Conductor	6708	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	3360	Modular degree for the optimal curve
Δ	-10934335152 = -1 · 24 · 37 · 132 · 432	Discriminant
Eigenvalues	2- 3+  2  0  0 13+ -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,543,1098]	[a1,a2,a3,a4,a6]
Generators	[11:91:1]	Generators of the group modulo torsion
j	1104595238912/683395947	j-invariant
L	3.956230402691	L(r)(E,1)/r!
Ω	0.79073416234737	Real period
R	1.6677456601203	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	26832p1 107328w1 20124e1 87204k1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 6708c1

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

---

Quadratic twists for elliptic curve 6708c1

-4	8	-3	13
26832p1	107328w1	20124e1	87204k1

---

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