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	121680dl	Isogeny class
Conductor	121680	Conductor
∏ cp	128	Product of Tamagawa factors cp
deg	1548288	Modular degree for the optimal curve
Δ	-8094214128343449600 = -1 · 218 · 39 · 52 · 137	Discriminant
Eigenvalues	2- 3- 5+  2  0 13+  0  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-146523,138573578]	[a1,a2,a3,a4,a6]
Generators	[221:-10816:1]	Generators of the group modulo torsion
j	-24137569/561600	j-invariant
L	6.6910672167977	L(r)(E,1)/r!
Ω	0.19569377943004	Real period
R	1.0684849166407	Regulator
r	1	Rank of the group of rational points
S	0.99999999485175	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	15210bf1 40560br1 9360cb1	Quadratic twists by: -4 -3 13

Hecke Eigenvalues for elliptic curve 121680dl1

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

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Quadratic twists for elliptic curve 121680dl1

-4	-3	13
15210bf1	40560br1	9360cb1

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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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