Cremona's table of elliptic curves

187 = 11 · 17

Field	Data	Notes
Atkin-Lehner	11- 17+	Signs for the Atkin-Lehner involutions
Class	187a	Isogeny class
Conductor	187	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	16	Modular degree for the optimal curve
Δ	-384659 = -1 · 113 · 172	Discriminant
Eigenvalues	0  1  3  2 11-  2 17+  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,11,30]	[a1,a2,a3,a4,a6]
j	134217728/384659	j-invariant
L	1.4097579515619	L(r)(E,1)/r!
Ω	2.1146369273428	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	2992f1 11968b1 1683h1 4675l1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 187a1

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	1	3	2	-	2	+	2	-3	-6	-7	-7	12	-10	0	6	-3	8	-7	-9	2	8	6	15	11

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Quadratic twists for elliptic curve 187a1

-4	8	-3	5	-7	-11	13	17	-19	-23
2992f1	11968b1	1683h1	4675l1	9163g1	2057e1	31603a1	3179a1	67507h1	98923b1

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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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