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	4312l	Isogeny class
Conductor	4312	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	3863552 = 210 · 73 · 11	Discriminant
Eigenvalues	2- -2 -4 7- 11- -2 -2 -8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1640,25024]	[a1,a2,a3,a4,a6]
Generators	[-40:168:1] [16:56:1]	Generators of the group modulo torsion
j	1389715708/11	j-invariant
L	2.998008850957	L(r)(E,1)/r!
Ω	2.2272534330575	Real period
R	1.3460564507214	Regulator
r	2	Rank of the group of rational points
S	0.99999999999951	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	8624c2 34496w2 38808ba2 107800q2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4312l2

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

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Quadratic twists for elliptic curve 4312l2

-4	8	-3	5	-7	-11
8624c2	34496w2	38808ba2	107800q2	4312k2	47432l2

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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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