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	122304ct	Isogeny class
Conductor	122304	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	291840	Modular degree for the optimal curve
Δ	-94314362688 = -1 · 26 · 34 · 72 · 135	Discriminant
Eigenvalues	2+ 3-  0 7-  3 13+ -3  5	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-52068,4555746]	[a1,a2,a3,a4,a6]
Generators	[129:48:1]	Generators of the group modulo torsion
j	-4978158127432000/30074733	j-invariant
L	8.6714105214754	L(r)(E,1)/r!
Ω	0.95192744765942	Real period
R	2.277329676506	Regulator
r	1	Rank of the group of rational points
S	1.0000000018144	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	122304m1 61152bh1 122304b1	Quadratic twists by: -4 8 -7

Hecke Eigenvalues for elliptic curve 122304ct1

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	-	3	+	-3	5	-6	-7	-8	4	8	6	-7	-1	9	-7	15	11	-14	-10	0	-12	2

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Quadratic twists for elliptic curve 122304ct1

-4	8	-7
122304m1	61152bh1	122304b1

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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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