Cremona's table of elliptic curves

3696 = 2⁴ · 3 · 7 · 11

Field	Data	Notes
Atkin-Lehner	2- 3+ 7+ 11-	Signs for the Atkin-Lehner involutions
Class	3696o	Isogeny class
Conductor	3696	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	288	Modular degree for the optimal curve
Δ	-33264 = -1 · 24 · 33 · 7 · 11	Discriminant
Eigenvalues	2- 3+  3 7+ 11- -1  0 -5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,6,-9]	[a1,a2,a3,a4,a6]
Generators	[5:11:1]	Generators of the group modulo torsion
j	1257728/2079	j-invariant
L	3.5370588442336	L(r)(E,1)/r!
Ω	1.9415900266249	Real period
R	1.8217331134431	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	924g1 14784ce1 11088bi1 92400hb1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3696o1

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
-	+	3	+	-	-1	0	-5	-6	-3	4	-7	-12	-2	-3	6	-3	2	1	-12	-7	4	0	6	2

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Quadratic twists for elliptic curve 3696o1

-4	8	-3	5	-7	-11
924g1	14784ce1	11088bi1	92400hb1	25872da1	40656bv1

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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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