Cremona's table of elliptic curves

994 = 2 · 7 · 71

Field	Data	Notes
Atkin-Lehner	2+ 7- 71+	Signs for the Atkin-Lehner involutions
Class	994c	Isogeny class
Conductor	994	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	576	Modular degree for the optimal curve
Δ	-442640128 = -1 · 28 · 73 · 712	Discriminant
Eigenvalues	2+  2 -2 7-  4  0  0  2	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-371,-3091]	[a1,a2,a3,a4,a6]
j	-5671177348537/442640128	j-invariant
L	1.6238833102939	L(r)(E,1)/r!
Ω	0.54129443676462	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	7952f1 31808k1 8946y1 24850r1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 994c1

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	-2	-	4	0	0	2	8	6	-8	6	12	-4	12	6	-4	0	4	+	-14	4	-14	6	-12

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Quadratic twists for elliptic curve 994c1

-4	8	-3	5	-7	-11	-71
7952f1	31808k1	8946y1	24850r1	6958d1	120274i1	70574d1

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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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