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	64	Product of Tamagawa factors cp
Δ	257586497888040000 = 26 · 312 · 54 · 594	Discriminant
Eigenvalues	2+ 3- 5+  0 -4 -2  6  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-2255805,1304404101]	[a1,a2,a3,a4,a6]
Generators	[-318:44763:1]	Generators of the group modulo torsion
j	1741409690685460393681/353342246760000	j-invariant
L	2.5542022277382	L(r)(E,1)/r!
Ω	0.30214312608946	Real period
R	2.1134042173956	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	42480bf4 1770h3 26550bt4	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 5310d4

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 5310d4

-4	-3	5
42480bf4	1770h3	26550bt4

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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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