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	121680dk	Isogeny class
Conductor	121680	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-3326427000000000000 = -1 · 212 · 39 · 512 · 132	Discriminant
Eigenvalues	2- 3- 5+ -1 -6 13+  0 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-463008,-149682832]	[a1,a2,a3,a4,a6]
Generators	[360002:76359375:8]	Generators of the group modulo torsion
j	-21752792449024/6591796875	j-invariant
L	3.8630021035132	L(r)(E,1)/r!
Ω	0.09010795755589	Real period
R	5.3588526041107	Regulator
r	1	Rank of the group of rational points
S	0.99999999987505	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	7605i2 40560bq2 121680et2	Quadratic twists by: -4 -3 13

Hecke Eigenvalues for elliptic curve 121680dk2

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
-	-	+	-1	-6	+	0	-4	-6	6	5	-2	0	-11	-6	0	-6	-1	11	6	-5	-11	-12	12	-17

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Quadratic twists for elliptic curve 121680dk2

-4	-3	13
7605i2	40560bq2	121680et2

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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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