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	15400m	Isogeny class
Conductor	15400	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	122880	Modular degree for the optimal curve
Δ	-119098502908000000 = -1 · 28 · 56 · 75 · 116	Discriminant
Eigenvalues	2- -2 5+ 7+ 11+  0 -4  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,95692,12109888]	[a1,a2,a3,a4,a6]
j	24226243449392/29774625727	j-invariant
L	0.88852421238637	L(r)(E,1)/r!
Ω	0.22213105309659	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	30800n1 123200v1 616b1 107800bs1	Quadratic twists by: -4 8 5 -7

Hecke Eigenvalues for elliptic curve 15400m1

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

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Quadratic twists for elliptic curve 15400m1

-4	8	5	-7
30800n1	123200v1	616b1	107800bs1

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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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