Cremona's table of elliptic curves

4312 = 2³ · 7² · 11

Field	Data	Notes
Atkin-Lehner	2- 7- 11+	Signs for the Atkin-Lehner involutions
Class	4312j	Isogeny class
Conductor	4312	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-10624768 = -1 · 28 · 73 · 112	Discriminant
Eigenvalues	2- -2  0 7- 11+  2 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,12,160]	[a1,a2,a3,a4,a6]
Generators	[2:14:1]	Generators of the group modulo torsion
j	2000/121	j-invariant
L	2.5432154555589	L(r)(E,1)/r!
Ω	1.7370331372257	Real period
R	0.36602863253675	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	8624h2 34496bp2 38808bc2 107800j2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4312j2

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

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Quadratic twists for elliptic curve 4312j2

-4	8	-3	5	-7	-11
8624h2	34496bp2	38808bc2	107800j2	4312i2	47432k2

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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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