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	121968co	Isogeny class
Conductor	121968	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	677376	Modular degree for the optimal curve
Δ	-71088367730688 = -1 · 219 · 33 · 73 · 114	Discriminant
Eigenvalues	2- 3+  0 7+ 11-  5 -6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-415635,-103138222]	[a1,a2,a3,a4,a6]
Generators	[386911:10078272:343]	Generators of the group modulo torsion
j	-4904170882875/43904	j-invariant
L	6.0594414564897	L(r)(E,1)/r!
Ω	0.094013733058075	Real period
R	8.0565908292477	Regulator
r	1	Rank of the group of rational points
S	1.0000000032771	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	15246c1 121968cn2 121968cz1	Quadratic twists by: -4 -3 -11

Hecke Eigenvalues for elliptic curve 121968co1

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	+	-	5	-6	-2	-3	3	-5	-4	-9	1	6	6	9	5	13	3	2	-8	-3	-3	-10

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Quadratic twists for elliptic curve 121968co1

-4	-3	-11
15246c1	121968cn2	121968cz1

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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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