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	4312a	Isogeny class
Conductor	4312	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	8064	Modular degree for the optimal curve
Δ	15714201868288 = 211 · 78 · 113	Discriminant
Eigenvalues	2+ -1  2 7+ 11+  3 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-9032,272812]	[a1,a2,a3,a4,a6]
Generators	[33:98:1]	Generators of the group modulo torsion
j	6902546/1331	j-invariant
L	3.4354474642291	L(r)(E,1)/r!
Ω	0.66257521266191	Real period
R	1.7283308111427	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	8624a1 34496e1 38808bz1 107800bj1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4312a1

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
+	-1	2	+	+	3	-2	4	-4	-7	-8	12	-8	8	-10	14	-9	-5	-3	-6	4	-17	-6	-2	7

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Quadratic twists for elliptic curve 4312a1

-4	8	-3	5	-7	-11
8624a1	34496e1	38808bz1	107800bj1	4312c1	47432p1

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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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