Cremona's table of elliptic curves

122304 = 2⁶ · 3 · 7² · 13

Field	Data	Notes
Atkin-Lehner	2- 3+ 7- 13+	Signs for the Atkin-Lehner involutions
Class	122304fl	Isogeny class
Conductor	122304	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	921600	Modular degree for the optimal curve
Δ	-43953678742192128 = -1 · 228 · 32 · 72 · 135	Discriminant
Eigenvalues	2- 3+ -2 7-  3 13+ -5 -1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-130209,20750913]	[a1,a2,a3,a4,a6]
Generators	[93:3072:1]	Generators of the group modulo torsion
j	-19007021070457/3421836288	j-invariant
L	4.0090495161008	L(r)(E,1)/r!
Ω	0.34633419685275	Real period
R	1.4469584681316	Regulator
r	1	Rank of the group of rational points
S	0.99999998118846	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	122304dk1 30576da1 122304gr1	Quadratic twists by: -4 8 -7

Hecke Eigenvalues for elliptic curve 122304fl1

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	-	3	+	-5	-1	0	1	4	2	-10	-10	-1	3	-3	-5	5	1	-12	6	-16	14	-4

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Quadratic twists for elliptic curve 122304fl1

-4	8	-7
122304dk1	30576da1	122304gr1

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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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