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	69696dn	Isogeny class
Conductor	69696	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	23040	Modular degree for the optimal curve
Δ	-152425152 = -1 · 26 · 39 · 112	Discriminant
Eigenvalues	2+ 3-  4 -1 11- -2  4 -3	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,132,-110]	[a1,a2,a3,a4,a6]
Generators	[155:1935:1]	Generators of the group modulo torsion
j	45056/27	j-invariant
L	8.4716894504345	L(r)(E,1)/r!
Ω	1.0644840541147	Real period
R	3.9792467614187	Regulator
r	1	Rank of the group of rational points
S	1.0000000000707	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	69696gz1 1089k1 23232cm1 69696dm1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 69696dn1

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
+	-	4	-1	-	-2	4	-3	-2	-6	-5	-3	-2	12	-2	6	-10	3	1	0	11	-11	-6	-12	5

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Quadratic twists for elliptic curve 69696dn1

-4	8	-3	-11
69696gz1	1089k1	23232cm1	69696dm1

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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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