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	15400j	Isogeny class
Conductor	15400	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	3840	Modular degree for the optimal curve
Δ	11858000 = 24 · 53 · 72 · 112	Discriminant
Eigenvalues	2+ -2 5- 7+ 11+  2 -6 -8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-63,-122]	[a1,a2,a3,a4,a6]
Generators	[-7:5:1] [-3:7:1]	Generators of the group modulo torsion
j	14047232/5929	j-invariant
L	5.0265407691028	L(r)(E,1)/r!
Ω	1.757421339338	Real period
R	0.71504491503967	Regulator
r	2	Rank of the group of rational points
S	0.99999999999991	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	30800x1 123200da1 15400x1 107800bd1	Quadratic twists by: -4 8 5 -7

Hecke Eigenvalues for elliptic curve 15400j1

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	-	+	+	2	-6	-8	-6	-6	0	4	-6	-8	2	-12	-4	6	-6	0	-14	0	-16	10	-16

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Quadratic twists for elliptic curve 15400j1

-4	8	5	-7
30800x1	123200da1	15400x1	107800bd1

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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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