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	12950g	Isogeny class
Conductor	12950	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	15840	Modular degree for the optimal curve
Δ	-212831242750 = -1 · 2 · 53 · 75 · 373	Discriminant
Eigenvalues	2+  0 5- 7+  0 -7 -4  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-1832,37926]	[a1,a2,a3,a4,a6]
Generators	[29:78:1]	Generators of the group modulo torsion
j	-5441560307469/1702649942	j-invariant
L	2.6860386064079	L(r)(E,1)/r!
Ω	0.94491965203215	Real period
R	0.47376843110969	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	103600cd1 116550fm1 12950q1 90650bi1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 12950g1

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	-7	-4	4	1	5	1	-	0	4	7	3	14	0	7	-15	7	14	-18	11	0

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Quadratic twists for elliptic curve 12950g1

-4	-3	5	-7
103600cd1	116550fm1	12950q1	90650bi1

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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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