Cremona's table of elliptic curves

774 = 2 · 3² · 43

Field	Data	Notes
Atkin-Lehner	2- 3+ 43-	Signs for the Atkin-Lehner involutions
Class	774f	Isogeny class
Conductor	774	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	-25038980496 = -1 · 24 · 39 · 433	Discriminant
Eigenvalues	2- 3+ -3 -1 -3 -1 -6 -1	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,511,6049]	[a1,a2,a3,a4,a6]
Generators	[109:1106:1]	Generators of the group modulo torsion
j	751089429/1272112	j-invariant
L	2.7370287348169	L(r)(E,1)/r!
Ω	0.81707645218251	Real period
R	0.13957428787243	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	6192j2 24768c2 774a1 19350b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 774f2

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
-	+	-3	-1	-3	-1	-6	-1	0	-3	-4	2	0	-	-3	0	0	14	-4	-6	2	14	9	-18	5

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Quadratic twists for elliptic curve 774f2

-4	8	-3	5	-7	-11	-43
6192j2	24768c2	774a1	19350b2	37926bf2	93654f2	33282e2

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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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