Cremona's table of elliptic curves

77616 = 2⁴ · 3² · 7² · 11

Field	Data	Notes
Atkin-Lehner	2+ 3- 7- 11+	Signs for the Atkin-Lehner involutions
Class	77616bt	Isogeny class
Conductor	77616	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	98304	Modular degree for the optimal curve
Δ	105663861072 = 24 · 36 · 77 · 11	Discriminant
Eigenvalues	2+ 3- -2 7- 11+ -2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-11466,472311]	[a1,a2,a3,a4,a6]
Generators	[79:244:1]	Generators of the group modulo torsion
j	121485312/77	j-invariant
L	4.045628308	L(r)(E,1)/r!
Ω	1.0479448909103	Real period
R	3.8605353599802	Regulator
r	1	Rank of the group of rational points
S	1.0000000003288	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	38808bh1 8624f1 11088l1	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 77616bt1

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
+	-	-2	-	+	-2	-2	-4	-8	2	-4	6	6	4	12	10	-8	-10	-4	-8	2	8	-12	10	-10

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Quadratic twists for elliptic curve 77616bt1

-4	-3	-7
38808bh1	8624f1	11088l1

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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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