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	15400f	Isogeny class
Conductor	15400	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	6912	Modular degree for the optimal curve
Δ	-1352243200 = -1 · 211 · 52 · 74 · 11	Discriminant
Eigenvalues	2+  2 5+ 7- 11-  5 -8 -1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-8,1772]	[a1,a2,a3,a4,a6]
Generators	[1:42:1]	Generators of the group modulo torsion
j	-1250/26411	j-invariant
L	7.2772924135281	L(r)(E,1)/r!
Ω	1.2166245811768	Real period
R	1.4953857841852	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	30800c1 123200bv1 15400s1 107800w1	Quadratic twists by: -4 8 5 -7

Hecke Eigenvalues for elliptic curve 15400f1

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	+	-	-	5	-8	-1	-3	1	1	-4	0	-7	-8	-2	8	-14	6	-13	-4	-4	9	-9	-7

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Quadratic twists for elliptic curve 15400f1

-4	8	5	-7
30800c1	123200bv1	15400s1	107800w1

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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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