Cremona's table of elliptic curves

812 = 2² · 7 · 29

Field	Data	Notes
Atkin-Lehner	2- 7- 29+	Signs for the Atkin-Lehner involutions
Class	812b	Isogeny class
Conductor	812	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	96	Modular degree for the optimal curve
Δ	-17825024 = -1 · 28 · 74 · 29	Discriminant
Eigenvalues	2- -1 -1 7-  1  1  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-36,232]	[a1,a2,a3,a4,a6]
Generators	[-6:14:1]	Generators of the group modulo torsion
j	-20720464/69629	j-invariant
L	1.9569919893896	L(r)(E,1)/r!
Ω	1.9151319254323	Real period
R	0.085154794621087	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	3248f1 12992q1 7308e1 20300a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 812b1

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	-1	-	1	1	2	-4	-6	+	-5	-4	-4	-11	3	3	2	-2	-4	-10	0	-15	-6	4	4

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Quadratic twists for elliptic curve 812b1

-4	8	-3	5	-7	-11	29
3248f1	12992q1	7308e1	20300a1	5684d1	98252g1	23548b1

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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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