Cremona's table of elliptic curves

854 = 2 · 7 · 61

Field	Data	Notes
Atkin-Lehner	2+ 7- 61-	Signs for the Atkin-Lehner involutions
Class	854b	Isogeny class
Conductor	854	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	29343216566272 = 236 · 7 · 61	Discriminant
Eigenvalues	2+  1  0 7- -3 -4 -3 -7	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-56176,-5122754]	[a1,a2,a3,a4,a6]
Generators	[-466185:493549:3375]	Generators of the group modulo torsion
j	19604918227371765625/29343216566272	j-invariant
L	2.00350282537	L(r)(E,1)/r!
Ω	0.31013573916253	Real period
R	3.2300418371324	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	6832e3 27328e3 7686t3 21350r3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 854b3

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	0	-	-3	-4	-3	-7	3	6	-4	2	6	-1	3	-6	6	-	-13	3	2	-1	9	-3	-10

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Quadratic twists for elliptic curve 854b3

-4	8	-3	5	-7	-11	61
6832e3	27328e3	7686t3	21350r3	5978b3	103334x3	52094g3

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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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