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	4312i	Isogeny class
Conductor	4312	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-1249993330432 = -1 · 28 · 79 · 112	Discriminant
Eigenvalues	2-  2  0 7- 11+ -2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,572,-53724]	[a1,a2,a3,a4,a6]
Generators	[132:1518:1]	Generators of the group modulo torsion
j	2000/121	j-invariant
L	4.9183279674968	L(r)(E,1)/r!
Ω	0.41160227936167	Real period
R	2.9873060804743	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	8624j2 34496bs2 38808bd2 107800k2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4312i2

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 4312i2

-4	8	-3	5	-7	-11
8624j2	34496bs2	38808bd2	107800k2	4312j2	47432i2

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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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