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	294a	Isogeny class
Conductor	294	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	84	Modular degree for the optimal curve
Δ	-34588806 = -1 · 2 · 3 · 78	Discriminant
Eigenvalues	2- 3+  1 7+  5  0 -4  8	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-50,293]	[a1,a2,a3,a4,a6]
j	-2401/6	j-invariant
L	1.8280004280168	L(r)(E,1)/r!
Ω	1.8280004280168	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	2352r1 9408v1 882c1 7350u1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 294a1

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
-	+	1	+	5	0	-4	8	-4	-5	3	-4	0	2	-6	-9	-11	-6	-2	2	10	3	-7	-6	7

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Quadratic twists for elliptic curve 294a1

-4	8	-3	5	-7	-11	13	17	-19
2352r1	9408v1	882c1	7350u1	294b1	35574d1	49686c1	84966dm1	106134u1

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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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