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	774b	Isogeny class
Conductor	774	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	480	Modular degree for the optimal curve
Δ	385191936 = 212 · 37 · 43	Discriminant
Eigenvalues	2+ 3-  2  4 -4  6  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-216,832]	[a1,a2,a3,a4,a6]
j	1532808577/528384	j-invariant
L	1.5541356319872	L(r)(E,1)/r!
Ω	1.5541356319872	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	6192w1 24768bf1 258d1 19350ck1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 774b1

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

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Quadratic twists for elliptic curve 774b1

-4	8	-3	5	-7	-11	-43
6192w1	24768bf1	258d1	19350ck1	37926o1	93654bq1	33282be1

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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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