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	121680n	Isogeny class
Conductor	121680	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	1032192	Modular degree for the optimal curve
Δ	-197612649617760000 = -1 · 28 · 39 · 54 · 137	Discriminant
Eigenvalues	2+ 3- 5+  0 -4 13+  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,127257,12333958]	[a1,a2,a3,a4,a6]
Generators	[-39:2704:1] [534:15250:1]	Generators of the group modulo torsion
j	253012016/219375	j-invariant
L	11.410295589951	L(r)(E,1)/r!
Ω	0.20660649787954	Real period
R	6.9033983104623	Regulator
r	2	Rank of the group of rational points
S	1.0000000002466	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	60840g1 40560z1 9360t1	Quadratic twists by: -4 -3 13

Hecke Eigenvalues for elliptic curve 121680n1

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
+	-	+	0	-4	+	2	-4	4	6	-4	-6	-2	-12	-8	-14	-12	-2	0	-8	2	-8	-12	6	10

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Quadratic twists for elliptic curve 121680n1

-4	-3	13
60840g1	40560z1	9360t1

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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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