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	7700b	Isogeny class
Conductor	7700	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	2641100000000 = 28 · 58 · 74 · 11	Discriminant
Eigenvalues	2- -2 5+ 7+ 11+ -4 -8 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-3508,-18012]	[a1,a2,a3,a4,a6]
Generators	[-37:250:1] [-32:250:1]	Generators of the group modulo torsion
j	1193895376/660275	j-invariant
L	4.0836944191315	L(r)(E,1)/r!
Ω	0.66430477063005	Real period
R	1.0245534378391	Regulator
r	2	Rank of the group of rational points
S	0.99999999999994	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	30800bw2 123200y2 69300bo2 1540b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 7700b2

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	-8	-4	-2	-6	-4	-10	2	-4	-2	-2	0	-2	-14	-4	16	-8	4	-2	2

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Quadratic twists for elliptic curve 7700b2

-4	8	-3	5	-7	-11
30800bw2	123200y2	69300bo2	1540b2	53900n2	84700v2

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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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