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	6825a	Isogeny class
Conductor	6825	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	914443359375 = 3 · 510 · 74 · 13	Discriminant
Eigenvalues	-1 3+ 5+ 7+  0 13+ -2  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-5838,-167844]	[a1,a2,a3,a4,a6]
Generators	[-39:68:1]	Generators of the group modulo torsion
j	1408317602329/58524375	j-invariant
L	1.9562505385535	L(r)(E,1)/r!
Ω	0.54757759488755	Real period
R	1.7862770106173	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	109200fw3 20475r4 1365e3 47775cr3	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 6825a3

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

---

Quadratic twists for elliptic curve 6825a3

-4	-3	5	-7	13
109200fw3	20475r4	1365e3	47775cr3	88725r3

---

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