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	13104ci	Isogeny class
Conductor	13104	Conductor
∏ cp	60	Product of Tamagawa factors cp
deg	46080	Modular degree for the optimal curve
Δ	-1925144771187456 = -1 · 28 · 310 · 73 · 135	Discriminant
Eigenvalues	2- 3-  1 7-  2 13-  4 -1	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-17832,2301388]	[a1,a2,a3,a4,a6]
Generators	[-22:1638:1]	Generators of the group modulo torsion
j	-3360132358144/10315633419	j-invariant
L	5.5323617946377	L(r)(E,1)/r!
Ω	0.41103105059321	Real period
R	0.2243286237805	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	3276g1 52416fw1 4368ba1 91728dz1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 13104ci1

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	-	4	-1	-3	-3	-5	-8	10	-1	-13	1	-8	-14	-2	4	-7	-17	-9	-5	13

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Quadratic twists for elliptic curve 13104ci1

-4	8	-3	-7
3276g1	52416fw1	4368ba1	91728dz1

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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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