Cremona's table of elliptic curves

7700 = 2² · 5² · 7 · 11

Field	Data	Notes
Atkin-Lehner	2- 5+ 7+ 11-	Signs for the Atkin-Lehner involutions
Class	7700d	Isogeny class
Conductor	7700	Conductor
∏ cp	48	Product of Tamagawa factors cp
Δ	17794411250000 = 24 · 57 · 76 · 112	Discriminant
Eigenvalues	2-  2 5+ 7+ 11-  4  0 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-4902133,-4175955738]	[a1,a2,a3,a4,a6]
Generators	[22266:488775:8]	Generators of the group modulo torsion
j	52112158467655991296/71177645	j-invariant
L	5.8014357453921	L(r)(E,1)/r!
Ω	0.10146196636937	Real period
R	4.7648690054228	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	30800bn3 123200h3 69300bb3 1540c3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 7700d3

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	0	-4	-6	-6	-4	-2	-6	4	-6	6	0	-10	-2	12	-8	-16	12	-18	10

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Quadratic twists for elliptic curve 7700d3

-4	8	-3	5	-7	-11
30800bn3	123200h3	69300bb3	1540c3	53900v3	84700t3

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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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