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	3135c	Isogeny class
Conductor	3135	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	624	Modular degree for the optimal curve
Δ	-1896675 = -1 · 3 · 52 · 113 · 19	Discriminant
Eigenvalues	2 3- 5+ -2 11+ -3 -3 19-	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,14,-59]	[a1,a2,a3,a4,a6]
Generators	[26:41:8]	Generators of the group modulo torsion
j	282300416/1896675	j-invariant
L	6.5661296033337	L(r)(E,1)/r!
Ω	1.3129308007691	Real period
R	2.5005619486904	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	50160bf1 9405n1 15675g1 34485o1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 3135c1

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
2	-	+	-2	+	-3	-3	-	-2	4	6	-8	0	-8	-8	-1	-9	-4	-8	1	-10	11	-9	3	12

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Quadratic twists for elliptic curve 3135c1

-4	-3	5	-11	-19
50160bf1	9405n1	15675g1	34485o1	59565a1

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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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