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	402c	Isogeny class
Conductor	402	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	48	Modular degree for the optimal curve
Δ	7236 = 22 · 33 · 67	Discriminant
Eigenvalues	2- 3+  2  2 -4  0  6  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-37,71]	[a1,a2,a3,a4,a6]
j	5611284433/7236	j-invariant
L	2.0887181251503	L(r)(E,1)/r!
Ω	4.1774362503006	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	3216k1 12864u1 1206b1 10050l1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 402c1

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
-	+	2	2	-4	0	6	4	-6	8	2	-2	-10	4	-6	-6	-8	8	+	-14	-6	-2	-12	-6	-2

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Quadratic twists for elliptic curve 402c1

-4	8	-3	5	-7	-11	13	17	-67
3216k1	12864u1	1206b1	10050l1	19698q1	48642f1	67938d1	116178bj1	26934c1

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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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