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	4	Product of Tamagawa factors cp
Δ	-52428800000000 = -1 · 227 · 58	Discriminant
Eigenvalues	2- -1 5- -2  3 -4 -3 -5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,8792,140912]	[a1,a2,a3,a4,a6]
Generators	[68:1024:1]	Generators of the group modulo torsion
j	46969655/32768	j-invariant
L	1.5552187610293	L(r)(E,1)/r!
Ω	0.39939334765617	Real period
R	0.97348814780971	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	50a4 1600v4 3600bo4 400b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 400c4

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 400c4

-4	8	-3	5	-7	-11	13	17
50a4	1600v4	3600bo4	400b2	19600dt4	48400cy4	67600da4	115600cr4

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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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