Cremona's table of elliptic curves

402 = 2 · 3 · 67

Field	Data	Notes
Atkin-Lehner	2+ 3- 67-	Signs for the Atkin-Lehner involutions
Class	402d	Isogeny class
Conductor	402	Conductor
∏ cp	18	Product of Tamagawa factors cp
Δ	-33261981696 = -1 · 212 · 33 · 673	Discriminant
Eigenvalues	2+ 3- -3 -1  0 -4 -6  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,800,1070]	[a1,a2,a3,a4,a6]
Generators	[25:179:1]	Generators of the group modulo torsion
j	56724909592967/33261981696	j-invariant
L	1.4143116144197	L(r)(E,1)/r!
Ω	0.70703921537878	Real period
R	1.0001649015055	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	3216d2 12864c2 1206f2 10050t2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 402d2

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
+	-	-3	-1	0	-4	-6	2	-9	0	5	-7	3	-1	0	9	-3	-10	-	-12	11	8	15	0	8

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Quadratic twists for elliptic curve 402d2

-4	8	-3	5	-7	-11	13	17	-67
3216d2	12864c2	1206f2	10050t2	19698e2	48642bc2	67938r2	116178g2	26934e2

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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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