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	13104bb	Isogeny class
Conductor	13104	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	3072	Modular degree for the optimal curve
Δ	-175292208 = -1 · 24 · 33 · 74 · 132	Discriminant
Eigenvalues	2- 3+  0 7+  4 13+  4  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,120,387]	[a1,a2,a3,a4,a6]
j	442368000/405769	j-invariant
L	2.3602907227589	L(r)(E,1)/r!
Ω	1.1801453613794	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	3276d1 52416dx1 13104bc1 91728cu1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 13104bb1

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
-	+	0	+	4	+	4	4	-4	8	8	-2	0	0	8	-8	0	-2	4	12	-2	-4	-8	-8	-10

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Quadratic twists for elliptic curve 13104bb1

-4	8	-3	-7
3276d1	52416dx1	13104bc1	91728cu1

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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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