Cremona's table of elliptic curves

102414 = 2 · 3 · 13² · 101

Field	Data	Notes
Atkin-Lehner	2- 3- 13+ 101+	Signs for the Atkin-Lehner involutions
Class	102414r	Isogeny class
Conductor	102414	Conductor
∏ cp	192	Product of Tamagawa factors cp
Δ	1261770673884741072 = 24 · 36 · 139 · 1012	Discriminant
Eigenvalues	2- 3-  0 -2  0 13+ -6  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-31674068,68609939904]	[a1,a2,a3,a4,a6]
Generators	[1134658:-2564402:343]	Generators of the group modulo torsion
j	728073347908550631625/261408867408	j-invariant
L	11.924369349335	L(r)(E,1)/r!
Ω	0.2202696716018	Real period
R	1.1278191830814	Regulator
r	1	Rank of the group of rational points
S	1.0000000014529	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	7878b2	Quadratic twists by: 13

Hecke Eigenvalues for elliptic curve 102414r2

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

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Quadratic twists for elliptic curve 102414r2

13
7878b2

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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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