Cremona's table of elliptic curves

770 = 2 · 5 · 7 · 11

Field	Data	Notes
Atkin-Lehner	2+ 5+ 7- 11+	Signs for the Atkin-Lehner involutions
Class	770b	Isogeny class
Conductor	770	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-2137096192000 = -1 · 218 · 53 · 72 · 113	Discriminant
Eigenvalues	2+ -2 5+ 7- 11+  2 -6  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,2271,56852]	[a1,a2,a3,a4,a6]
j	1296134247276791/2137096192000	j-invariant
L	0.56315565348231	L(r)(E,1)/r!
Ω	0.56315565348231	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	6160f3 24640w3 6930bk3 3850o3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 770b3

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

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Quadratic twists for elliptic curve 770b3

-4	8	-3	5	-7	-11
6160f3	24640w3	6930bk3	3850o3	5390p3	8470u3

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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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