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	4312h	Isogeny class
Conductor	4312	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-12346872896512 = -1 · 210 · 77 · 114	Discriminant
Eigenvalues	2-  0  2 7- 11+ -2  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,5341,77518]	[a1,a2,a3,a4,a6]
Generators	[3297:43120:27]	Generators of the group modulo torsion
j	139863132/102487	j-invariant
L	3.9465879138963	L(r)(E,1)/r!
Ω	0.45377344864722	Real period
R	4.3486324791169	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	8624f4 34496be3 38808bh3 107800h3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4312h4

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

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Quadratic twists for elliptic curve 4312h4

-4	8	-3	5	-7	-11
8624f4	34496be3	38808bh3	107800h3	616e4	47432f3

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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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