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	121680ed	Isogeny class
Conductor	121680	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	69120	Modular degree for the optimal curve
Δ	1232010000 = 24 · 36 · 54 · 132	Discriminant
Eigenvalues	2- 3- 5+  5  5 13+  1 -3	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-273,403]	[a1,a2,a3,a4,a6]
Generators	[-42:775:27]	Generators of the group modulo torsion
j	1141504/625	j-invariant
L	9.2656697939298	L(r)(E,1)/r!
Ω	1.3353761200115	Real period
R	3.4693108860806	Regulator
r	1	Rank of the group of rational points
S	0.99999999715008	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	30420n1 13520x1 121680fm1	Quadratic twists by: -4 -3 13

Hecke Eigenvalues for elliptic curve 121680ed1

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
-	-	+	5	5	+	1	-3	3	1	0	-7	-5	-5	-12	-2	11	-13	3	-13	2	4	-12	7	-11

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Quadratic twists for elliptic curve 121680ed1

-4	-3	13
30420n1	13520x1	121680fm1

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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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