Cremona's table of elliptic curves

3536 = 2⁴ · 13 · 17

Field	Data	Notes
Atkin-Lehner	2- 13+ 17+	Signs for the Atkin-Lehner involutions
Class	3536g	Isogeny class
Conductor	3536	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	1152	Modular degree for the optimal curve
Δ	47071232 = 214 · 132 · 17	Discriminant
Eigenvalues	2- -2 -2 -2 -4 13+ 17+  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-144,532]	[a1,a2,a3,a4,a6]
Generators	[-12:26:1] [-1:26:1]	Generators of the group modulo torsion
j	81182737/11492	j-invariant
L	2.9356752541056	L(r)(E,1)/r!
Ω	1.9354546312883	Real period
R	0.75839423116614	Regulator
r	2	Rank of the group of rational points
S	0.99999999999995	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	442d1 14144u1 31824be1 88400br1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3536g1

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

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Quadratic twists for elliptic curve 3536g1

-4	8	-3	5	13	17
442d1	14144u1	31824be1	88400br1	45968l1	60112q1

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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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