Cremona's table of elliptic curves

12688 = 2⁴ · 13 · 61

Field	Data	Notes
Atkin-Lehner	2- 13+ 61+	Signs for the Atkin-Lehner involutions
Class	12688b	Isogeny class
Conductor	12688	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	117504	Modular degree for the optimal curve
Δ	792086727098368 = 228 · 13 · 613	Discriminant
Eigenvalues	2-  0  2 -4 -4 13+ -6 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-982219,-374677638]	[a1,a2,a3,a4,a6]
j	25585196494633455393/193380548608	j-invariant
L	0.15165183473462	L(r)(E,1)/r!
Ω	0.15165183473462	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	1586c1 50752m1 114192bj1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 12688b1

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
-	0	2	-4	-4	+	-6	-6	-2	2	-4	-6	-6	2	2	-6	4	+	8	-4	2	-14	6	6	2

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Quadratic twists for elliptic curve 12688b1

-4	8	-3
1586c1	50752m1	114192bj1

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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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