Cremona's table of elliptic curves

5270 = 2 · 5 · 17 · 31

Field	Data	Notes
Atkin-Lehner	2+ 5- 17- 31+	Signs for the Atkin-Lehner involutions
Class	5270c	Isogeny class
Conductor	5270	Conductor
∏ cp	70	Product of Tamagawa factors cp
deg	67200	Modular degree for the optimal curve
Δ	845979197740000000 = 28 · 57 · 175 · 313	Discriminant
Eigenvalues	2+  1 5- -2 -2  3 17- -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-357093,-69222192]	[a1,a2,a3,a4,a6]
Generators	[-381:3590:1]	Generators of the group modulo torsion
j	5035771024411098786121/845979197740000000	j-invariant
L	3.2964077258633	L(r)(E,1)/r!
Ω	0.19753302608429	Real period
R	0.23839830672573	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	42160w1 47430ba1 26350m1 89590c1	Quadratic twists by: -4 -3 5 17

Hecke Eigenvalues for elliptic curve 5270c1

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	-	-2	-2	3	-	-2	7	-3	+	6	-10	-4	1	5	6	2	5	-1	-14	-2	-16	12	-14

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Quadratic twists for elliptic curve 5270c1

-4	-3	5	17
42160w1	47430ba1	26350m1	89590c1

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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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