Cremona's table of elliptic curves

75690 = 2 · 3² · 5 · 29²

Field	Data	Notes
Atkin-Lehner	2- 3- 5- 29-	Signs for the Atkin-Lehner involutions
Class	75690bq	Isogeny class
Conductor	75690	Conductor
∏ cp	36	Product of Tamagawa factors cp
deg	1336320	Modular degree for the optimal curve
Δ	5907810087786817800 = 23 · 310 · 52 · 298	Discriminant
Eigenvalues	2- 3- 5-  1  2  0 -7  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-461867,-30231309]	[a1,a2,a3,a4,a6]
Generators	[-3362:77367:8]	Generators of the group modulo torsion
j	29878729/16200	j-invariant
L	11.836004630745	L(r)(E,1)/r!
Ω	0.1952507155911	Real period
R	1.6838755513475	Regulator
r	1	Rank of the group of rational points
S	1.0000000001296	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	25230b1 75690o1	Quadratic twists by: -3 29

Hecke Eigenvalues for elliptic curve 75690bq1

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	0	-7	4	-3	-	5	-6	-10	2	3	-4	0	6	8	-3	9	-9	-12	-11	11

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Quadratic twists for elliptic curve 75690bq1

-3	29
25230b1	75690o1

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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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