Cremona's table of elliptic curves

400 = 2⁴ · 5²

Field	Data	Notes
Atkin-Lehner	2- 5-	Signs for the Atkin-Lehner involutions
Class	400c	Isogeny class
Conductor	400	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	-51200000000 = -1 · 217 · 58	Discriminant
Eigenvalues	2- -1 5- -2  3 -4 -3 -5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1208,-19088]	[a1,a2,a3,a4,a6]
Generators	[92:800:1]	Generators of the group modulo torsion
j	-121945/32	j-invariant
L	1.5552187610293	L(r)(E,1)/r!
Ω	0.39939334765617	Real period
R	0.3244960492699	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	50a3 1600v3 3600bo3 400b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 400c3

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	-	-2	3	-4	-3	-5	-6	0	-2	2	-3	4	-12	6	0	2	13	-12	11	10	9	15	2

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Quadratic twists for elliptic curve 400c3

-4	8	-3	5	-7	-11	13	17
50a3	1600v3	3600bo3	400b1	19600dt3	48400cy3	67600da3	115600cr3

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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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