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	69696do	Isogeny class
Conductor	69696	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	5160960	Modular degree for the optimal curve
Δ	2036127821347749888 = 216 · 313 · 117	Discriminant
Eigenvalues	2+ 3-  4  2 11-  0 -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-34919148,-79422473680]	[a1,a2,a3,a4,a6]
Generators	[62222265862510:133041985578720:9116230969]	Generators of the group modulo torsion
j	55635379958596/24057	j-invariant
L	9.8219952275707	L(r)(E,1)/r!
Ω	0.062106013913977	Real period
R	19.768607354587	Regulator
r	1	Rank of the group of rational points
S	1.0000000000182	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	69696hb1 8712n1 23232be1 6336u1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 69696do1

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

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Quadratic twists for elliptic curve 69696do1

-4	8	-3	-11
69696hb1	8712n1	23232be1	6336u1

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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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