Cremona's table of elliptic curves

7878 = 2 · 3 · 13 · 101

Field	Data	Notes
Atkin-Lehner	2+ 3- 13- 101+	Signs for the Atkin-Lehner involutions
Class	7878b	Isogeny class
Conductor	7878	Conductor
∏ cp	36	Product of Tamagawa factors cp
deg	14976	Modular degree for the optimal curve
Δ	-3369653284608 = -1 · 28 · 33 · 136 · 101	Discriminant
Eigenvalues	2+ 3-  0  2  0 13- -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-11661,491656]	[a1,a2,a3,a4,a6]
Generators	[-1464:27245:27]	Generators of the group modulo torsion
j	-175338610176327625/3369653284608	j-invariant
L	3.9775191569509	L(r)(E,1)/r!
Ω	0.79419359538989	Real period
R	5.0082488451675	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	63024k1 23634m1 102414r1	Quadratic twists by: -4 -3 13

Hecke Eigenvalues for elliptic curve 7878b1

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	0	-	-6	-4	0	6	-4	2	6	-4	-6	6	12	-10	-10	-6	-4	8	0	-6	-10

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Quadratic twists for elliptic curve 7878b1

-4	-3	13
63024k1	23634m1	102414r1

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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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