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	3536l	Isogeny class
Conductor	3536	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	1536	Modular degree for the optimal curve
Δ	11767808 = 212 · 132 · 17	Discriminant
Eigenvalues	2- -2  2 -2  6 13+ 17- -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-952,-11628]	[a1,a2,a3,a4,a6]
Generators	[54:312:1]	Generators of the group modulo torsion
j	23320116793/2873	j-invariant
L	2.7672932587403	L(r)(E,1)/r!
Ω	0.85942012392078	Real period
R	1.6099769959514	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	221b1 14144be1 31824w1 88400bk1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3536l1

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	6	+	-	-4	-6	-6	2	2	-6	0	4	14	-4	2	0	10	10	-14	-12	-18	2

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Quadratic twists for elliptic curve 3536l1

-4	8	-3	5	13	17
221b1	14144be1	31824w1	88400bk1	45968v1	60112t1

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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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