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	121680cz	Isogeny class
Conductor	121680	Conductor
∏ cp	192	Product of Tamagawa factors cp
Δ	-3.1618023938842E+20	Discriminant
Eigenvalues	2- 3+ 5- -4  0 13+ -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-6064227,5811245154]	[a1,a2,a3,a4,a6]
Generators	[663:45630:1]	Generators of the group modulo torsion
j	-63378025803/812500	j-invariant
L	4.6037152723331	L(r)(E,1)/r!
Ω	0.17249298345527	Real period
R	0.55602687131746	Regulator
r	1	Rank of the group of rational points
S	1.0000000096488	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	15210e3 121680cm1 9360bb3	Quadratic twists by: -4 -3 13

Hecke Eigenvalues for elliptic curve 121680cz3

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

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Quadratic twists for elliptic curve 121680cz3

-4	-3	13
15210e3	121680cm1	9360bb3

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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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