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	15400r	Isogeny class
Conductor	15400	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	677600000000 = 211 · 58 · 7 · 112	Discriminant
Eigenvalues	2-  2 5+ 7- 11+ -6 -2  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-7008,-219988]	[a1,a2,a3,a4,a6]
Generators	[34062:346375:216]	Generators of the group modulo torsion
j	1189646642/21175	j-invariant
L	6.7853816953823	L(r)(E,1)/r!
Ω	0.52235408366259	Real period
R	6.495002056656	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	30800g2 123200ci2 3080a2 107800bu2	Quadratic twists by: -4 8 5 -7

Hecke Eigenvalues for elliptic curve 15400r2

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
-	2	+	-	+	-6	-2	2	6	0	0	4	-8	4	4	-8	-4	14	-8	12	-2	6	0	-2	-12

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Quadratic twists for elliptic curve 15400r2

-4	8	5	-7
30800g2	123200ci2	3080a2	107800bu2

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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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