Cremona's table of elliptic curves

121968 = 2⁴ · 3² · 7 · 11²

Field	Data	Notes
Atkin-Lehner	2+ 3- 7- 11+	Signs for the Atkin-Lehner involutions
Class	121968bs	Isogeny class
Conductor	121968	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	675840	Modular degree for the optimal curve
Δ	-36964168910355456 = -1 · 210 · 37 · 7 · 119	Discriminant
Eigenvalues	2+ 3- -2 7- 11+  2 -4  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,51909,-8052550]	[a1,a2,a3,a4,a6]
Generators	[8068:45009:64]	Generators of the group modulo torsion
j	8788/21	j-invariant
L	5.6124070687703	L(r)(E,1)/r!
Ω	0.18904664149297	Real period
R	7.4219872410593	Regulator
r	1	Rank of the group of rational points
S	1.0000000043237	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	60984o1 40656o1 121968ba1	Quadratic twists by: -4 -3 -11

Hecke Eigenvalues for elliptic curve 121968bs1

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	-	+	2	-4	4	-6	-2	2	2	0	6	-12	0	-12	-2	-4	-6	10	16	6	6	-6

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Quadratic twists for elliptic curve 121968bs1

-4	-3	-11
60984o1	40656o1	121968ba1

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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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