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	69696dt	Isogeny class
Conductor	69696	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1419264	Modular degree for the optimal curve
Δ	-7680866267086848 = -1 · 214 · 37 · 118	Discriminant
Eigenvalues	2+ 3- -4 -5 11-  2 -4 -3	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-894432,-325615840]	[a1,a2,a3,a4,a6]
Generators	[1369:31869:1]	Generators of the group modulo torsion
j	-30908416/3	j-invariant
L	1.9201075044267	L(r)(E,1)/r!
Ω	0.077621172357689	Real period
R	6.1842260510795	Regulator
r	1	Rank of the group of rational points
S	0.99999999978524	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	69696hd1 4356l1 23232bd1 69696ds1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 69696dt1

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	-5	-	2	-4	-3	-6	-2	1	-7	10	-4	2	-2	-6	-7	-9	-8	-3	1	-14	-4	13

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Quadratic twists for elliptic curve 69696dt1

-4	8	-3	-11
69696hd1	4356l1	23232bd1	69696ds1

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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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