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	13104cl	Isogeny class
Conductor	13104	Conductor
∏ cp	28	Product of Tamagawa factors cp
deg	221760	Modular degree for the optimal curve
Δ	-65470711556210688 = -1 · 223 · 36 · 77 · 13	Discriminant
Eigenvalues	2- 3- -4 7- -1 13- -4 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-663627,208445690]	[a1,a2,a3,a4,a6]
Generators	[773:12544:1]	Generators of the group modulo torsion
j	-10824513276632329/21926008832	j-invariant
L	3.3085292207482	L(r)(E,1)/r!
Ω	0.34900120413703	Real period
R	0.33857120400499	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	1638r1 52416ge1 1456l1 91728eu1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 13104cl1

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
-	-	-4	-	-1	-	-4	-2	-7	8	-3	7	7	8	3	0	-6	-13	-7	4	9	13	-16	6	11

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Quadratic twists for elliptic curve 13104cl1

-4	8	-3	-7
1638r1	52416ge1	1456l1	91728eu1

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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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