Cremona's table of elliptic curves

8400 = 2⁴ · 3 · 5² · 7

Field	Data	Notes
Atkin-Lehner	2- 3- 5- 7+	Signs for the Atkin-Lehner involutions
Class	8400cp	Isogeny class
Conductor	8400	Conductor
∏ cp	28	Product of Tamagawa factors cp
deg	80640	Modular degree for the optimal curve
Δ	-51267448968750000 = -1 · 24 · 314 · 59 · 73	Discriminant
Eigenvalues	2- 3- 5- 7+  4 -6  2 -6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-76833,13607838]	[a1,a2,a3,a4,a6]
j	-1605176213504/1640558367	j-invariant
L	2.2657386681026	L(r)(E,1)/r!
Ω	0.32367695258609	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	2100i1 33600fq1 25200fg1 8400bw1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 8400cp1

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
-	-	-	+	4	-6	2	-6	-2	6	2	-4	8	4	-4	6	-4	14	-4	0	-10	0	16	8	10

---

Quadratic twists for elliptic curve 8400cp1

-4	8	-3	5	-7
2100i1	33600fq1	25200fg1	8400bw1	58800hk1

---

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