Cremona's table of elliptic curves

121680 = 2⁴ · 3² · 5 · 13²

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 13+	Signs for the Atkin-Lehner involutions
Class	121680z	Isogeny class
Conductor	121680	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	856321481676960000 = 28 · 38 · 54 · 138	Discriminant
Eigenvalues	2+ 3- 5+ -4 -4 13+  6  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-237783,3088982]	[a1,a2,a3,a4,a6]
Generators	[-419:5400:1] [589:8208:1]	Generators of the group modulo torsion
j	1650587344/950625	j-invariant
L	9.6493416035445	L(r)(E,1)/r!
Ω	0.23973109234507	Real period
R	10.062672216909	Regulator
r	2	Rank of the group of rational points
S	0.99999999934346	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	60840q2 40560l2 9360v2	Quadratic twists by: -4 -3 13

Hecke Eigenvalues for elliptic curve 121680z2

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	0	-8	-6	-4	2	-10	4	8	2	-12	-2	-16	8	6	16	-4	-2	-2

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Quadratic twists for elliptic curve 121680z2

-4	-3	13
60840q2	40560l2	9360v2

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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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