Cremona's table of elliptic curves

3135 = 3 · 5 · 11 · 19

Field	Data	Notes
Atkin-Lehner	3+ 5- 11- 19+	Signs for the Atkin-Lehner involutions
Class	3135b	Isogeny class
Conductor	3135	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	72572506875 = 34 · 54 · 11 · 194	Discriminant
Eigenvalues	-1 3+ 5-  0 11- -2 -2 19+	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-4940,-135070]	[a1,a2,a3,a4,a6]
Generators	[-42:43:1]	Generators of the group modulo torsion
j	13332452758522561/72572506875	j-invariant
L	1.9523265426857	L(r)(E,1)/r!
Ω	0.56965208393256	Real period
R	0.85680654813369	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	50160ca3 9405e4 15675s3 34485h3	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 3135b3

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

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Quadratic twists for elliptic curve 3135b3

-4	-3	5	-11	-19
50160ca3	9405e4	15675s3	34485h3	59565u3

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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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