Cremona's table of elliptic curves

15400 = 2³ · 5² · 7 · 11

Field	Data	Notes
Atkin-Lehner	2+ 5+ 7+ 11+	Signs for the Atkin-Lehner involutions
Class	15400c	Isogeny class
Conductor	15400	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	422576000000 = 210 · 56 · 74 · 11	Discriminant
Eigenvalues	2+  0 5+ 7+ 11+ -2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-6275,188750]	[a1,a2,a3,a4,a6]
Generators	[55:100:1]	Generators of the group modulo torsion
j	1707831108/26411	j-invariant
L	4.1374334358724	L(r)(E,1)/r!
Ω	0.94555705220705	Real period
R	1.0939142768316	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	30800m4 123200k4 616e3 107800h4	Quadratic twists by: -4 8 5 -7

Hecke Eigenvalues for elliptic curve 15400c3

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	+	+	+	-2	2	-4	8	-2	-4	-6	6	4	12	10	8	10	-4	-8	2	-8	-12	10	-10

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Quadratic twists for elliptic curve 15400c3

-4	8	5	-7
30800m4	123200k4	616e3	107800h4

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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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