Cremona's table of elliptic curves

5310 = 2 · 3² · 5 · 59

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 59-	Signs for the Atkin-Lehner involutions
Class	5310d	Isogeny class
Conductor	5310	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	214114134375000 = 23 · 39 · 58 · 592	Discriminant
Eigenvalues	2+ 3- 5+  0 -4 -2  6  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-36091125,83463328125]	[a1,a2,a3,a4,a6]
Generators	[4461:103704:1]	Generators of the group modulo torsion
j	7131771986839837165458001/293709375000	j-invariant
L	2.5542022277382	L(r)(E,1)/r!
Ω	0.30214312608946	Real period
R	4.2268084347912	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	42480bf6 1770h5 26550bt6	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 5310d5

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
+	-	+	0	-4	-2	6	4	-8	2	0	6	6	4	0	-6	-	-10	12	16	-6	0	-4	-2	-14

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Quadratic twists for elliptic curve 5310d5

-4	-3	5
42480bf6	1770h5	26550bt6

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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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