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	12950r	Isogeny class
Conductor	12950	Conductor
∏ cp	224	Product of Tamagawa factors cp
Δ	-1973003142250000000 = -1 · 27 · 59 · 78 · 372	Discriminant
Eigenvalues	2-  2 5- 7-  4 -2 -6  8	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-146013,-70971469]	[a1,a2,a3,a4,a6]
j	-176265952176509/1010177608832	j-invariant
L	6.1317200711294	L(r)(E,1)/r!
Ω	0.10949500127017	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	103600bv2 116550cq2 12950i2 90650dc2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 12950r2

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 12950r2

-4	-3	5	-7
103600bv2	116550cq2	12950i2	90650dc2

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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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