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	121680bh	Isogeny class
Conductor	121680	Conductor
∏ cp	256	Product of Tamagawa factors cp
Δ	20267964063360000 = 210 · 38 · 54 · 136	Discriminant
Eigenvalues	2+ 3- 5-  0  4 13+  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-304707,-64376494]	[a1,a2,a3,a4,a6]
Generators	[-335:324:1]	Generators of the group modulo torsion
j	868327204/5625	j-invariant
L	8.403871078141	L(r)(E,1)/r!
Ω	0.20328177499639	Real period
R	2.5838122526578	Regulator
r	1	Rank of the group of rational points
S	1.0000000026771	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	60840bs4 40560a4 720c3	Quadratic twists by: -4 -3 13

Hecke Eigenvalues for elliptic curve 121680bh4

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

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Quadratic twists for elliptic curve 121680bh4

-4	-3	13
60840bs4	40560a4	720c3

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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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