Cremona's table of elliptic curves

13104 = 2⁴ · 3² · 7 · 13

Field	Data	Notes
Atkin-Lehner	2+ 3- 7+ 13+	Signs for the Atkin-Lehner involutions
Class	13104o	Isogeny class
Conductor	13104	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	55635600384 = 210 · 38 · 72 · 132	Discriminant
Eigenvalues	2+ 3- -2 7+ -4 13+ -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1011,4930]	[a1,a2,a3,a4,a6]
Generators	[-27:112:1] [-21:130:1]	Generators of the group modulo torsion
j	153091012/74529	j-invariant
L	5.797226347778	L(r)(E,1)/r!
Ω	0.99313784780189	Real period
R	1.4593206674702	Regulator
r	2	Rank of the group of rational points
S	1.0000000000002	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	6552v2 52416fi2 4368f2 91728bo2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 13104o2

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

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Quadratic twists for elliptic curve 13104o2

-4	8	-3	-7
6552v2	52416fi2	4368f2	91728bo2

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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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