Cremona's table of elliptic curves

12138 = 2 · 3 · 7 · 17²

Field	Data	Notes
Atkin-Lehner	2- 3+ 7+ 17-	Signs for the Atkin-Lehner involutions
Class	12138r	Isogeny class
Conductor	12138	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	29376	Modular degree for the optimal curve
Δ	-8203490750616 = -1 · 23 · 3 · 72 · 178	Discriminant
Eigenvalues	2- 3+  1 7+ -3  0 17-  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-26305,-1658857]	[a1,a2,a3,a4,a6]
Generators	[757:19942:1]	Generators of the group modulo torsion
j	-288568081/1176	j-invariant
L	5.9720318242303	L(r)(E,1)/r!
Ω	0.18739326439747	Real period
R	5.3114963367124	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	97104cy1 36414bb1 84966eb1 12138z1	Quadratic twists by: -4 -3 -7 17

Hecke Eigenvalues for elliptic curve 12138r1

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	+	-3	0	-	0	4	-3	-5	4	0	6	12	-7	7	-6	6	-12	3	-5	-8	-16	-7

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Quadratic twists for elliptic curve 12138r1

-4	-3	-7	17
97104cy1	36414bb1	84966eb1	12138z1

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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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