Cremona's table of elliptic curves

6864 = 2⁴ · 3 · 11 · 13

Field	Data	Notes
Atkin-Lehner	2+ 3+ 11+ 13+	Signs for the Atkin-Lehner involutions
Class	6864c	Isogeny class
Conductor	6864	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	188457984 = 210 · 32 · 112 · 132	Discriminant
Eigenvalues	2+ 3+ -2  0 11+ 13+ -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-144,144]	[a1,a2,a3,a4,a6]
Generators	[-10:22:1]	Generators of the group modulo torsion
j	324730948/184041	j-invariant
L	2.8786231795406	L(r)(E,1)/r!
Ω	1.5440626669224	Real period
R	0.93215879161112	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	3432d2 27456cm2 20592i2 75504g2	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 6864c2

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

---

Quadratic twists for elliptic curve 6864c2

-4	8	-3	-11	13
3432d2	27456cm2	20592i2	75504g2	89232h2

---

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