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	3696g	Isogeny class
Conductor	3696	Conductor
∏ cp	128	Product of Tamagawa factors cp
Δ	-193602081835008 = -1 · 211 · 32 · 72 · 118	Discriminant
Eigenvalues	2+ 3+ -2 7- 11- -2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,13936,212640]	[a1,a2,a3,a4,a6]
Generators	[-4:396:1]	Generators of the group modulo torsion
j	146142660369886/94532266521	j-invariant
L	2.7369092524238	L(r)(E,1)/r!
Ω	0.35349927929381	Real period
R	0.96779166632651	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	1848j6 14784cl6 11088v6 92400by5	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3696g6

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

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Quadratic twists for elliptic curve 3696g6

-4	8	-3	5	-7	-11
1848j6	14784cl6	11088v6	92400by5	25872w5	40656l5

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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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