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	69696bm	Isogeny class
Conductor	69696	Conductor
∏ cp	64	Product of Tamagawa factors cp
deg	368640	Modular degree for the optimal curve
Δ	1571086281904128 = 212 · 39 · 117	Discriminant
Eigenvalues	2+ 3-  0 -2 11-  4 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-428340,-107885536]	[a1,a2,a3,a4,a6]
Generators	[-380:108:1]	Generators of the group modulo torsion
j	1643032000/297	j-invariant
L	5.7423806880715	L(r)(E,1)/r!
Ω	0.1866195369088	Real period
R	1.9231576657051	Regulator
r	1	Rank of the group of rational points
S	1.000000000078	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	69696bk1 34848bs1 23232h1 6336x1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 69696bm1

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

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Quadratic twists for elliptic curve 69696bm1

-4	8	-3	-11
69696bk1	34848bs1	23232h1	6336x1

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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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