Cremona's table of elliptic curves

12978 = 2 · 3² · 7 · 103

Field	Data	Notes
Atkin-Lehner	2+ 3- 7+ 103-	Signs for the Atkin-Lehner involutions
Class	12978g	Isogeny class
Conductor	12978	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	30720	Modular degree for the optimal curve
Δ	6083190424836 = 22 · 316 · 73 · 103	Discriminant
Eigenvalues	2+ 3-  2 7+ -4 -4  4  6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-5166,-78368]	[a1,a2,a3,a4,a6]
Generators	[-19:122:1]	Generators of the group modulo torsion
j	20917350641377/8344568484	j-invariant
L	3.6230085282295	L(r)(E,1)/r!
Ω	0.58285897194512	Real period
R	3.1079632489303	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	103824ca1 4326e1 90846bl1	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 12978g1

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	+	-4	-4	4	6	-4	6	0	4	12	-6	-12	-6	0	-8	2	-2	2	-8	0	14	-14

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Quadratic twists for elliptic curve 12978g1

-4	-3	-7
103824ca1	4326e1	90846bl1

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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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