Cremona's table of elliptic curves

6105 = 3 · 5 · 11 · 37

Field	Data	Notes
Atkin-Lehner	3+ 5+ 11+ 37-	Signs for the Atkin-Lehner involutions
Class	6105c	Isogeny class
Conductor	6105	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	640	Modular degree for the optimal curve
Δ	201465 = 32 · 5 · 112 · 37	Discriminant
Eigenvalues	-1 3+ 5+ -2 11+ -2 -6 -6	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-31,-76]	[a1,a2,a3,a4,a6]
Generators	[-4:3:1] [6:-2:1]	Generators of the group modulo torsion
j	3301293169/201465	j-invariant
L	2.8006631527456	L(r)(E,1)/r!
Ω	2.0306807348952	Real period
R	1.3791745322732	Regulator
r	2	Rank of the group of rational points
S	1.0000000000001	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	97680cp1 18315r1 30525u1 67155c1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 6105c1

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	+	-2	-6	-6	0	-4	0	-	2	-4	-8	-2	0	4	-4	-8	-4	-10	6	-6	-14

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Quadratic twists for elliptic curve 6105c1

-4	-3	5	-11
97680cp1	18315r1	30525u1	67155c1

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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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