Cremona's table of elliptic curves

7770 = 2 · 3 · 5 · 7 · 37

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5- 7- 37+	Signs for the Atkin-Lehner involutions
Class	7770i	Isogeny class
Conductor	7770	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	1517578125000 = 23 · 3 · 512 · 7 · 37	Discriminant
Eigenvalues	2+ 3+ 5- 7- -4  2 -2  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-33477,2342949]	[a1,a2,a3,a4,a6]
Generators	[113:81:1]	Generators of the group modulo torsion
j	4149383532674367961/1517578125000	j-invariant
L	2.8099838644169	L(r)(E,1)/r!
Ω	0.83257011799209	Real period
R	1.1250239083741	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	62160cr4 23310bm4 38850cn4 54390t4	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 7770i4

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
+	+	-	-	-4	2	-2	4	-8	6	0	+	-2	4	-8	6	-4	-2	0	0	14	-4	4	-14	-6

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Quadratic twists for elliptic curve 7770i4

-4	-3	5	-7
62160cr4	23310bm4	38850cn4	54390t4

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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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