Cremona's table of elliptic curves

29748 = 2² · 3 · 37 · 67

Field	Data	Notes
Atkin-Lehner	2- 3+ 37+ 67-	Signs for the Atkin-Lehner involutions
Class	29748a	Isogeny class
Conductor	29748	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	3564594488740608 = 28 · 34 · 376 · 67	Discriminant
Eigenvalues	2- 3+  0  0  4 -4 -6  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-45828,-2435832]	[a1,a2,a3,a4,a6]
Generators	[-58:154:1]	Generators of the group modulo torsion
j	41580138984946000/13924197221643	j-invariant
L	4.3433352925874	L(r)(E,1)/r!
Ω	0.33509952291919	Real period
R	4.3204431276126	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	118992o2 89244b2	Quadratic twists by: -4 -3

Hecke Eigenvalues for elliptic curve 29748a2

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

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Quadratic twists for elliptic curve 29748a2

-4	-3
118992o2	89244b2

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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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