Cremona's table of elliptic curves

3612 = 2² · 3 · 7 · 43

Field	Data	Notes
Atkin-Lehner	2- 3+ 7+ 43-	Signs for the Atkin-Lehner involutions
Class	3612d	Isogeny class
Conductor	3612	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	51744982169647872 = 28 · 32 · 710 · 433	Discriminant
Eigenvalues	2- 3+ -2 7+  2 -6  2  8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-440844,112275720]	[a1,a2,a3,a4,a6]
Generators	[357:516:1]	Generators of the group modulo torsion
j	37011742745030294992/202128836600187	j-invariant
L	2.5445349808876	L(r)(E,1)/r!
Ω	0.35733063378551	Real period
R	2.3736513099285	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	14448bc2 57792be2 10836c2 90300bl2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3612d2

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

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Quadratic twists for elliptic curve 3612d2

-4	8	-3	5	-7
14448bc2	57792be2	10836c2	90300bl2	25284l2

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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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