Cremona's table of elliptic curves

69696 = 2⁶ · 3² · 11²

Field	Data	Notes
Atkin-Lehner	2- 3+ 11-	Signs for the Atkin-Lehner involutions
Class	69696ee	Isogeny class
Conductor	69696	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	737280	Modular degree for the optimal curve
Δ	564953144421777408 = 230 · 33 · 117	Discriminant
Eigenvalues	2- 3+  0  2 11-  2  6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-500940,131587984]	[a1,a2,a3,a4,a6]
Generators	[-667:12999:1]	Generators of the group modulo torsion
j	1108717875/45056	j-invariant
L	7.4811224011582	L(r)(E,1)/r!
Ω	0.28860956921963	Real period
R	6.4803138902109	Regulator
r	1	Rank of the group of rational points
S	1.0000000000149	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	69696k1 17424bc1 69696ef3 6336bi1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 69696ee1

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

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Quadratic twists for elliptic curve 69696ee1

-4	8	-3	-11
69696k1	17424bc1	69696ef3	6336bi1

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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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