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
deg	144	Modular degree for the optimal curve
Δ	-21100176 = -1 · 24 · 39 · 67	Discriminant
Eigenvalues	2+ 3- -3 -1  0 -4 -6  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-145,692]	[a1,a2,a3,a4,a6]
Generators	[-5:38:1]	Generators of the group modulo torsion
j	-333822098953/21100176	j-invariant
L	1.4143116144197	L(r)(E,1)/r!
Ω	2.1211176461363	Real period
R	0.33338830050183	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	3216d1 12864c1 1206f1 10050t1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 402d1

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 402d1

-4	8	-3	5	-7	-11	13	17	-67
3216d1	12864c1	1206f1	10050t1	19698e1	48642bc1	67938r1	116178g1	26934e1

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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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