Cremona's table of elliptic curves

400 = 2⁴ · 5²

Field	Data	Notes
Atkin-Lehner	2+ 5+	Signs for the Atkin-Lehner involutions
Class	400a	Isogeny class
Conductor	400	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	80000000 = 210 · 57	Discriminant
Eigenvalues	2+  0 5+ -4 -4  2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-2675,53250]	[a1,a2,a3,a4,a6]
Generators	[-15:300:1]	Generators of the group modulo torsion
j	132304644/5	j-invariant
L	1.6854886295926	L(r)(E,1)/r!
Ω	1.8057642614567	Real period
R	0.93339350299966	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	200c3 1600p3 3600p3 80a3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 400a3

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

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Quadratic twists for elliptic curve 400a3

-4	8	-3	5	-7	-11	13	17
200c3	1600p3	3600p3	80a3	19600i3	48400k4	67600b4	115600b4

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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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