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	6825d	Isogeny class
Conductor	6825	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	-102478206796875 = -1 · 38 · 57 · 7 · 134	Discriminant
Eigenvalues	-1 3+ 5+ 7-  4 13- -6  8	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-2463,-490344]	[a1,a2,a3,a4,a6]
Generators	[105:597:1]	Generators of the group modulo torsion
j	-105756712489/6558605235	j-invariant
L	2.4188084802488	L(r)(E,1)/r!
Ω	0.26262190734467	Real period
R	1.1512788978198	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	109200ft3 20475ba4 1365c4 47775cj3	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 6825d4

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

---

Quadratic twists for elliptic curve 6825d4

-4	-3	5	-7	13
109200ft3	20475ba4	1365c4	47775cj3	88725f3

---

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