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	8400o	Isogeny class
Conductor	8400	Conductor
∏ cp	132	Product of Tamagawa factors cp
deg	665280	Modular degree for the optimal curve
Δ	-3.1135777825975E+22	Discriminant
Eigenvalues	2+ 3+ 5- 7- -2 -3 -5 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,4941792,-7363325088]	[a1,a2,a3,a4,a6]
Generators	[1292:34300:1]	Generators of the group modulo torsion
j	16683494528422270/38919722282469	j-invariant
L	3.4918479621942	L(r)(E,1)/r!
Ω	0.060707285938497	Real period
R	0.43575319245512	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	4200bd1 33600hi1 25200ck1 8400t1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 8400o1

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	-3	-5	-4	5	9	5	10	1	-3	-12	11	-5	9	4	4	-6	-14	-5	-6	-18

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Quadratic twists for elliptic curve 8400o1

-4	8	-3	5	-7
4200bd1	33600hi1	25200ck1	8400t1	58800ek1

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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