Cremona's table of elliptic curves

308 = 2² · 7 · 11

Field	Data	Notes
Atkin-Lehner	2- 7+ 11-	Signs for the Atkin-Lehner involutions
Class	308a	Isogeny class
Conductor	308	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	24	Modular degree for the optimal curve
Δ	-137984 = -1 · 28 · 72 · 11	Discriminant
Eigenvalues	2- -1 -1 7+ 11- -4 -6 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-21,49]	[a1,a2,a3,a4,a6]
Generators	[7:-14:1]	Generators of the group modulo torsion
j	-4194304/539	j-invariant
L	1.389106382029	L(r)(E,1)/r!
Ω	3.1762112277545	Real period
R	0.072891163004243	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	1232g1 4928b1 2772g1 7700h1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 308a1

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	+	-	-4	-6	-2	1	2	-1	-9	6	8	-8	10	1	-2	11	11	-14	-14	4	13	-9

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Quadratic twists for elliptic curve 308a1

-4	8	-3	5	-7	-11	13	17	-19
1232g1	4928b1	2772g1	7700h1	2156b1	3388f1	52052g1	89012o1	111188h1

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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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