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	15400b	Isogeny class
Conductor	15400	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	12320000000 = 211 · 57 · 7 · 11	Discriminant
Eigenvalues	2+  0 5+ 7+ 11+  2 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-410675,101296750]	[a1,a2,a3,a4,a6]
Generators	[1270:40350:1]	Generators of the group modulo torsion
j	239369344910082/385	j-invariant
L	4.3428095613375	L(r)(E,1)/r!
Ω	0.81509361240294	Real period
R	5.3279887061495	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	30800l4 123200l4 3080e4 107800i4	Quadratic twists by: -4 8 5 -7

Hecke Eigenvalues for elliptic curve 15400b4

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

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Quadratic twists for elliptic curve 15400b4

-4	8	5	-7
30800l4	123200l4	3080e4	107800i4

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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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