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	121680r	Isogeny class
Conductor	121680	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	138240	Modular degree for the optimal curve
Δ	-306563512320 = -1 · 211 · 311 · 5 · 132	Discriminant
Eigenvalues	2+ 3- 5+  2 -1 13+ -6 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1443,-33982]	[a1,a2,a3,a4,a6]
Generators	[53:196:1] [61:324:1]	Generators of the group modulo torsion
j	-1316978/1215	j-invariant
L	11.937445679171	L(r)(E,1)/r!
Ω	0.37310774357159	Real period
R	1.9996646214061	Regulator
r	2	Rank of the group of rational points
S	1.0000000002083	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	60840k1 40560j1 121680bm1	Quadratic twists by: -4 -3 13

Hecke Eigenvalues for elliptic curve 121680r1

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	-1	+	-6	-6	-5	-3	-7	11	-10	1	-13	-10	-3	10	8	-4	-6	7	-10	-2	10

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Quadratic twists for elliptic curve 121680r1

-4	-3	13
60840k1	40560j1	121680bm1

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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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