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	3612b	Isogeny class
Conductor	3612	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	4032	Modular degree for the optimal curve
Δ	-155345199408 = -1 · 24 · 37 · 74 · 432	Discriminant
Eigenvalues	2- 3+  0 7+ -6 -2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,27,18954]	[a1,a2,a3,a4,a6]
j	131072000/9709074963	j-invariant
L	0.81146279680284	L(r)(E,1)/r!
Ω	0.81146279680284	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	14448be1 57792bi1 10836b1 90300br1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3612b1

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	+	-6	-2	-6	4	6	4	-8	-2	2	+	10	2	6	-2	12	4	-10	0	2	16	14

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Quadratic twists for elliptic curve 3612b1

-4	8	-3	5	-7
14448be1	57792bi1	10836b1	90300br1	25284h1

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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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