Cremona's table of elliptic curves

12614 = 2 · 7 · 17 · 53

Field	Data	Notes
Atkin-Lehner	2- 7- 17+ 53+	Signs for the Atkin-Lehner involutions
Class	12614i	Isogeny class
Conductor	12614	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	34512251171564852 = 22 · 74 · 176 · 533	Discriminant
Eigenvalues	2- -2  0 7-  0  2 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-3181058,-2184009776]	[a1,a2,a3,a4,a6]
Generators	[7726560:-173740988:3375]	Generators of the group modulo torsion
j	3559905615417290169486625/34512251171564852	j-invariant
L	5.0785372672464	L(r)(E,1)/r!
Ω	0.11304644503959	Real period
R	11.231085739732	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	100912k4 113526r4 88298u4	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 12614i4

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

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Quadratic twists for elliptic curve 12614i4

-4	-3	-7
100912k4	113526r4	88298u4

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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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