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	7700i	Isogeny class
Conductor	7700	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	126000	Modular degree for the optimal curve
Δ	3.27520882997E+19	Discriminant
Eigenvalues	2-  0 5- 7+ 11+ -1  3  1	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1733000,-833817500]	[a1,a2,a3,a4,a6]
Generators	[-295512:1524202:343]	Generators of the group modulo torsion
j	5755981643735040/327520882997	j-invariant
L	3.8306964182176	L(r)(E,1)/r!
Ω	0.13205021612214	Real period
R	9.6697971693697	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	30800cv1 123200ct1 69300ch1 7700f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 7700i1

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	-	+	+	-1	3	1	4	4	2	-7	3	0	-12	3	0	-3	11	1	5	-6	4	-18	16

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Quadratic twists for elliptic curve 7700i1

-4	8	-3	5	-7	-11
30800cv1	123200ct1	69300ch1	7700f1	53900ba1	84700bh1

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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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