Cremona's table of elliptic curves

1407 = 3 · 7 · 67

Field	Data	Notes
Atkin-Lehner	3- 7+ 67-	Signs for the Atkin-Lehner involutions
Class	1407c	Isogeny class
Conductor	1407	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	676049990758443 = 36 · 712 · 67	Discriminant
Eigenvalues	-1 3-  2 7+ -4  2 -6 -8	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-262947,-51904818]	[a1,a2,a3,a4,a6]
Generators	[-294:252:1]	Generators of the group modulo torsion
j	2010612953066556130993/676049990758443	j-invariant
L	2.2342596264526	L(r)(E,1)/r!
Ω	0.21083429425869	Real period
R	3.5324101870435	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	22512o4 90048c4 4221d4 35175h4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1407c3

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	-	2	+	-4	2	-6	-8	0	-2	8	-10	6	4	-4	-2	0	-14	-	0	2	-8	16	-14	-18

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Quadratic twists for elliptic curve 1407c3

-4	8	-3	5	-7	-67
22512o4	90048c4	4221d4	35175h4	9849j4	94269g4

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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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