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	3135g	Isogeny class
Conductor	3135	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	-12518055 = -1 · 32 · 5 · 114 · 19	Discriminant
Eigenvalues	1 3- 5-  4 11-  2  6 19+	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-23,173]	[a1,a2,a3,a4,a6]
j	-1263214441/12518055	j-invariant
L	3.8381648367394	L(r)(E,1)/r!
Ω	1.9190824183697	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	50160bm1 9405f1 15675h1 34485r1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 3135g1

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	-	-	4	-	2	6	+	0	-6	-4	2	6	-8	0	2	-8	6	12	-12	14	-16	0	18	14

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Quadratic twists for elliptic curve 3135g1

-4	-3	5	-11	-19
50160bm1	9405f1	15675h1	34485r1	59565l1

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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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