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	4312d	Isogeny class
Conductor	4312	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	64934718464 = 210 · 78 · 11	Discriminant
Eigenvalues	2+  2 -2 7- 11+ -4  0  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-11384,471164]	[a1,a2,a3,a4,a6]
j	1354435492/539	j-invariant
L	2.1681114075415	L(r)(E,1)/r!
Ω	1.0840557037707	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	8624k2 34496bt2 38808cm2 107800bt2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4312d2

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	4	4	10	-2	10	0	4	2	2	-6	0	-8	12	12	16	4	6	10

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Quadratic twists for elliptic curve 4312d2

-4	8	-3	5	-7	-11
8624k2	34496bt2	38808cm2	107800bt2	616c2	47432y2

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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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