Cremona's table of elliptic curves

11774 = 2 · 7 · 29²

Field	Data	Notes
Atkin-Lehner	2+ 7- 29-	Signs for the Atkin-Lehner involutions
Class	11774d	Isogeny class
Conductor	11774	Conductor
∏ cp	40	Product of Tamagawa factors cp
deg	24640	Modular degree for the optimal curve
Δ	-27557155391444 = -1 · 22 · 710 · 293	Discriminant
Eigenvalues	2+ -1 -1 7- -5  1  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-6078,309016]	[a1,a2,a3,a4,a6]
Generators	[466:9714:1]	Generators of the group modulo torsion
j	-1018411856981/1129900996	j-invariant
L	2.1713219791519	L(r)(E,1)/r!
Ω	0.60450476246489	Real period
R	0.089797554708182	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	94192w1 105966ch1 82418f1 11774m1	Quadratic twists by: -4 -3 -7 29

Hecke Eigenvalues for elliptic curve 11774d1

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
+	-1	-1	-	-5	1	2	-4	4	-	5	-2	0	-1	-7	9	10	0	2	-2	-4	1	-6	6	-12

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Quadratic twists for elliptic curve 11774d1

-4	-3	-7	29
94192w1	105966ch1	82418f1	11774m1

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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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