Cremona's table of elliptic curves

7800 = 2³ · 3 · 5² · 13

Field	Data	Notes
Atkin-Lehner	2- 3+ 5+ 13-	Signs for the Atkin-Lehner involutions
Class	7800o	Isogeny class
Conductor	7800	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	3422250000000000 = 210 · 34 · 512 · 132	Discriminant
Eigenvalues	2- 3+ 5+  0  0 13- -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-122408,16282812]	[a1,a2,a3,a4,a6]
Generators	[173:504:1]	Generators of the group modulo torsion
j	12677589459076/213890625	j-invariant
L	3.5740805758407	L(r)(E,1)/r!
Ω	0.44637782407821	Real period
R	4.003425330572	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	15600r2 62400bz2 23400n2 1560c2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 7800o2

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	0	-	-2	0	-4	6	8	-10	-6	-4	8	-2	0	6	-12	8	-6	8	12	-14	10

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Quadratic twists for elliptic curve 7800o2

-4	8	-3	5	13
15600r2	62400bz2	23400n2	1560c2	101400b2

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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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