Cremona's table of elliptic curves

38688 = 2⁵ · 3 · 13 · 31

Field	Data	Notes
Atkin-Lehner	2- 3+ 13+ 31+	Signs for the Atkin-Lehner involutions
Class	38688c	Isogeny class
Conductor	38688	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	10830163968 = 212 · 38 · 13 · 31	Discriminant
Eigenvalues	2- 3+  2  0  0 13+  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-2257,-40223]	[a1,a2,a3,a4,a6]
j	310563811648/2644083	j-invariant
L	1.3859695288876	L(r)(E,1)/r!
Ω	0.69298476443842	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	38688b3 77376v1 116064c3	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 38688c3

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

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Quadratic twists for elliptic curve 38688c3

-4	8	-3
38688b3	77376v1	116064c3

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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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