Cremona's table of elliptic curves

12726 = 2 · 3² · 7 · 101

Field	Data	Notes
Atkin-Lehner	2+ 3+ 7+ 101-	Signs for the Atkin-Lehner involutions
Class	12726b	Isogeny class
Conductor	12726	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	4672	Modular degree for the optimal curve
Δ	-267246 = -1 · 2 · 33 · 72 · 101	Discriminant
Eigenvalues	2+ 3+ -3 7+ -4  4 -4 -6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-231,1411]	[a1,a2,a3,a4,a6]
Generators	[-3:47:1] [-1:41:1]	Generators of the group modulo torsion
j	-50611941099/9898	j-invariant
L	4.1745293154463	L(r)(E,1)/r!
Ω	3.0101075502218	Real period
R	0.34670931568032	Regulator
r	2	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	101808r1 12726g1 89082f1	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 12726b1

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
+	+	-3	+	-4	4	-4	-6	-8	0	7	-8	9	-12	-4	-14	0	-5	7	-8	2	7	-14	-7	-19

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Quadratic twists for elliptic curve 12726b1

-4	-3	-7
101808r1	12726g1	89082f1

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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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