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	402a	Isogeny class
Conductor	402	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	32	Modular degree for the optimal curve
Δ	-51456 = -1 · 28 · 3 · 67	Discriminant
Eigenvalues	2+ 3+  1 -3  0 -4  2 -2	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-2,-12]	[a1,a2,a3,a4,a6]
Generators	[4:6:1]	Generators of the group modulo torsion
j	-1771561/51456	j-invariant
L	1.2440174085812	L(r)(E,1)/r!
Ω	1.5449271648358	Real period
R	0.40261361082137	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	3216j1 12864s1 1206d1 10050bj1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 402a1

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
+	+	1	-3	0	-4	2	-2	-3	0	-9	-3	3	-7	-8	-3	3	6	+	4	11	0	9	16	0

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Quadratic twists for elliptic curve 402a1

-4	8	-3	5	-7	-11	13	17	-67
3216j1	12864s1	1206d1	10050bj1	19698h1	48642o1	67938p1	116178k1	26934h1

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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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