Cremona's table of elliptic curves

294 = 2 · 3 · 7²

Field	Data	Notes
Atkin-Lehner	2+ 3- 7-	Signs for the Atkin-Lehner involutions
Class	294g	Isogeny class
Conductor	294	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	9001692 = 22 · 38 · 73	Discriminant
Eigenvalues	2+ 3- -4 7- -4 -4  0 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-138,592]	[a1,a2,a3,a4,a6]
Generators	[-1:27:1]	Generators of the group modulo torsion
j	838561807/26244	j-invariant
L	1.2377532022838	L(r)(E,1)/r!
Ω	2.300521848052	Real period
R	0.067253936499881	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	2352q2 9408s2 882k2 7350bv2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 294g2

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

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Quadratic twists for elliptic curve 294g2

-4	8	-3	5	-7	-11	13	17	-19
2352q2	9408s2	882k2	7350bv2	294f2	35574di2	49686dk2	84966be2	106134ci2

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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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