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	13104g	Isogeny class
Conductor	13104	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	10752	Modular degree for the optimal curve
Δ	458535168 = 28 · 39 · 7 · 13	Discriminant
Eigenvalues	2+ 3+  4 7+  4 13-  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-783,-8370]	[a1,a2,a3,a4,a6]
j	10536048/91	j-invariant
L	3.6119805798828	L(r)(E,1)/r!
Ω	0.9029951449707	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	6552r1 52416dt1 13104h1 91728d1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 13104g1

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	+	4	-	6	-4	-6	0	0	-6	12	-4	6	-8	14	-14	-4	12	6	-8	6	16	10

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Quadratic twists for elliptic curve 13104g1

-4	8	-3	-7
6552r1	52416dt1	13104h1	91728d1

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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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