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	770d	Isogeny class
Conductor	770	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	3368750000 = 24 · 58 · 72 · 11	Discriminant
Eigenvalues	2+ -2 5- 7+ 11-  0  0  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-848,9006]	[a1,a2,a3,a4,a6]
Generators	[5:67:1]	Generators of the group modulo torsion
j	67324767141241/3368750000	j-invariant
L	1.3476401146559	L(r)(E,1)/r!
Ω	1.3934589959707	Real period
R	0.12088982511799	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	6160o2 24640c2 6930w2 3850u2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 770d2

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	-	+	-	0	0	0	-4	2	-2	-6	8	-12	-6	-6	-10	-4	-8	-4	-4	-16	0	-6	14

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Quadratic twists for elliptic curve 770d2

-4	8	-3	5	-7	-11
6160o2	24640c2	6930w2	3850u2	5390j2	8470bg2

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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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