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	121680dz	Isogeny class
Conductor	121680	Conductor
∏ cp	128	Product of Tamagawa factors cp
Δ	1050691257044582400 = 214 · 312 · 52 · 136	Discriminant
Eigenvalues	2- 3- 5+ -4  0 13+ -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-450723,105513122]	[a1,a2,a3,a4,a6]
Generators	[-559:13520:1]	Generators of the group modulo torsion
j	702595369/72900	j-invariant
L	3.9339291905919	L(r)(E,1)/r!
Ω	0.26837064320126	Real period
R	1.8323209646028	Regulator
r	1	Rank of the group of rational points
S	0.99999998576971	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	15210n2 40560bv2 720j2	Quadratic twists by: -4 -3 13

Hecke Eigenvalues for elliptic curve 121680dz2

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	0	+	-6	-4	0	6	8	-2	-6	4	0	6	0	-10	-4	0	-2	-8	-12	18	-2

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Quadratic twists for elliptic curve 121680dz2

-4	-3	13
15210n2	40560bv2	720j2

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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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