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	12978h	Isogeny class
Conductor	12978	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	6144	Modular degree for the optimal curve
Δ	681189264 = 24 · 310 · 7 · 103	Discriminant
Eigenvalues	2+ 3- -2 7+  0  2  2 -8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-243,805]	[a1,a2,a3,a4,a6]
Generators	[-13:47:1]	Generators of the group modulo torsion
j	2181825073/934416	j-invariant
L	2.7487778126686	L(r)(E,1)/r!
Ω	1.4550184675367	Real period
R	0.94458519736939	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	103824cc1 4326d1 90846bf1	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 12978h1

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	2	2	-8	8	2	-8	2	2	-4	8	2	-4	2	4	-16	14	-8	12	10	2

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Quadratic twists for elliptic curve 12978h1

-4	-3	-7
103824cc1	4326d1	90846bf1

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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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