Cremona's table of elliptic curves

12950 = 2 · 5² · 7 · 37

Field	Data	Notes
Atkin-Lehner	2+ 5- 7+ 37-	Signs for the Atkin-Lehner involutions
Class	12950i	Isogeny class
Conductor	12950	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-126272201104000 = -1 · 27 · 53 · 78 · 372	Discriminant
Eigenvalues	2+ -2 5- 7+  4  2  6  8	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-5841,-567772]	[a1,a2,a3,a4,a6]
Generators	[20054:993587:8]	Generators of the group modulo torsion
j	-176265952176509/1010177608832	j-invariant
L	2.6167177093964	L(r)(E,1)/r!
Ω	0.24483826603652	Real period
R	5.343767850827	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	103600ch2 116550fp2 12950r2 90650bp2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 12950i2

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	-	+	4	2	6	8	0	-8	2	-	6	-12	-8	-10	0	-8	-14	-12	-8	2	-2	14	2

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Quadratic twists for elliptic curve 12950i2

-4	-3	5	-7
103600ch2	116550fp2	12950r2	90650bp2

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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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