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	774c	Isogeny class
Conductor	774	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	6080	Modular degree for the optimal curve
Δ	-145733640824196 = -1 · 22 · 325 · 43	Discriminant
Eigenvalues	2+ 3- -3 -1  1  1 -4  1	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-397116,-96224252]	[a1,a2,a3,a4,a6]
j	-9500554530751882177/199908972324	j-invariant
L	0.7607283477883	L(r)(E,1)/r!
Ω	0.095091043473537	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	6192y1 24768bg1 258e1 19350cb1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 774c1

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	1	1	-4	1	4	9	2	2	8	+	11	-4	12	0	2	-12	4	14	-3	10	17

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Quadratic twists for elliptic curve 774c1

-4	8	-3	5	-7	-11	-43
6192y1	24768bg1	258e1	19350cb1	37926p1	93654br1	33282bf1

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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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