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	121680cn	Isogeny class
Conductor	121680	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	50688	Modular degree for the optimal curve
Δ	-186900480 = -1 · 213 · 33 · 5 · 132	Discriminant
Eigenvalues	2- 3+ 5+ -4  5 13+ -2 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,117,442]	[a1,a2,a3,a4,a6]
Generators	[-3:8:1] [-1:18:1]	Generators of the group modulo torsion
j	9477/10	j-invariant
L	10.485553888626	L(r)(E,1)/r!
Ω	1.1887575330227	Real period
R	1.1025749147779	Regulator
r	2	Rank of the group of rational points
S	1.000000000316	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	15210bb1 121680da1 121680cy1	Quadratic twists by: -4 -3 13

Hecke Eigenvalues for elliptic curve 121680cn1

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	5	+	-2	-6	-9	-5	-3	5	-2	7	-9	4	-1	-4	-12	14	-16	-17	6	4	-2

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Quadratic twists for elliptic curve 121680cn1

-4	-3	13
15210bb1	121680da1	121680cy1

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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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