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
deg	1536	Modular degree for the optimal curve
Δ	144943568 = 24 · 77 · 11	Discriminant
Eigenvalues	2-  0  2 7- 11+ -2  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1274,17493]	[a1,a2,a3,a4,a6]
Generators	[642:685:27]	Generators of the group modulo torsion
j	121485312/77	j-invariant
L	3.9465879138963	L(r)(E,1)/r!
Ω	1.8150937945889	Real period
R	4.3486324791169	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	8624f1 34496be1 38808bh1 107800h1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4312h1

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 4312h1

-4	8	-3	5	-7	-11
8624f1	34496be1	38808bh1	107800h1	616e1	47432f1

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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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