Cremona's table of elliptic curves

851 = 23 · 37

Field	Data	Notes
Atkin-Lehner	23+ 37+	Signs for the Atkin-Lehner involutions
Class	851a	Isogeny class
Conductor	851	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	88	Modular degree for the optimal curve
Δ	19573 = 232 · 37	Discriminant
Eigenvalues	-2  1  0 -3  1  4  0  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-28,48]	[a1,a2,a3,a4,a6]
Generators	[6:11:1]	Generators of the group modulo torsion
j	2515456000/19573	j-invariant
L	1.403960360018	L(r)(E,1)/r!
Ω	3.8742025615056	Real period
R	0.18119346339397	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	13616h1 54464f1 7659c1 21275b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 851a1

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	1	0	-3	1	4	0	2	+	-8	2	+	3	-6	-13	7	14	-10	-12	-7	-9	-10	11	-4	-16

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Quadratic twists for elliptic curve 851a1

-4	8	-3	5	-7	-11	-23	37
13616h1	54464f1	7659c1	21275b1	41699d1	102971a1	19573b1	31487b1

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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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