Cremona's table of elliptic curves

121275 = 3² · 5² · 7² · 11

Field	Data	Notes
Atkin-Lehner	3- 5+ 7- 11+	Signs for the Atkin-Lehner involutions
Class	121275cx	Isogeny class
Conductor	121275	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	3686400	Modular degree for the optimal curve
Δ	-1.8355809343706E+21	Discriminant
Eigenvalues	0 3- 5+ 7- 11+  0 -3  3	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-1447950,2167663531]	[a1,a2,a3,a4,a6]
Generators	[-1085:49612:1]	Generators of the group modulo torsion
j	-250523582464/1369738755	j-invariant
L	5.2151368174245	L(r)(E,1)/r!
Ω	0.12845194018859	Real period
R	1.2687470926175	Regulator
r	1	Rank of the group of rational points
S	0.99999999931995	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	40425t1 24255bc1 17325i1	Quadratic twists by: -3 5 -7

Hecke Eigenvalues for elliptic curve 121275cx1

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	-	+	-	+	0	-3	3	-1	7	-6	8	-2	5	6	-3	-5	7	-6	10	12	-16	3	3	-1

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Quadratic twists for elliptic curve 121275cx1

-3	5	-7
40425t1	24255bc1	17325i1

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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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