Cremona's table of elliptic curves

10400 = 2⁵ · 5² · 13

Field	Data	Notes
Atkin-Lehner	2+ 5+ 13+	Signs for the Atkin-Lehner involutions
Class	10400a	Isogeny class
Conductor	10400	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-45697600000000 = -1 · 212 · 58 · 134	Discriminant
Eigenvalues	2+  0 5+  4 -4 13+ -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-2300,-328000]	[a1,a2,a3,a4,a6]
Generators	[685:17875:1]	Generators of the group modulo torsion
j	-21024576/714025	j-invariant
L	4.652285829328	L(r)(E,1)/r!
Ω	0.27824418257587	Real period
R	4.180038721977	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	10400b4 20800cw1 93600do2 2080f4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 10400a4

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	4	0	6	-4	-6	10	-8	-12	10	12	6	-4	-4	-2	-8	12	-6	-10

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Quadratic twists for elliptic curve 10400a4

-4	8	-3	5
10400b4	20800cw1	93600do2	2080f4

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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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