Cremona's table of elliptic curves

6825 = 3 · 5² · 7 · 13

Field	Data	Notes
Atkin-Lehner	3- 5+ 7- 13+	Signs for the Atkin-Lehner involutions
Class	6825j	Isogeny class
Conductor	6825	Conductor
∏ cp	160	Product of Tamagawa factors cp
Δ	191009675390625 = 310 · 58 · 72 · 132	Discriminant
Eigenvalues	-1 3- 5+ 7-  0 13+ -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-26963,1566792]	[a1,a2,a3,a4,a6]
Generators	[-53:1714:1]	Generators of the group modulo torsion
j	138742439989609/12224619225	j-invariant
L	3.1808664773633	L(r)(E,1)/r!
Ω	0.55261027283636	Real period
R	0.57560755449532	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	109200ct2 20475w2 1365a2 47775q2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 6825j2

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

---

Quadratic twists for elliptic curve 6825j2

-4	-3	5	-7	13
109200ct2	20475w2	1365a2	47775q2	88725bm2

---

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