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	12950c	Isogeny class
Conductor	12950	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	23040	Modular degree for the optimal curve
Δ	-239575000000 = -1 · 26 · 58 · 7 · 372	Discriminant
Eigenvalues	2+ -2 5+ 7- -4 -2 -4  8	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-2376,-50602]	[a1,a2,a3,a4,a6]
j	-94881210481/15332800	j-invariant
L	0.67783426533766	L(r)(E,1)/r!
Ω	0.33891713266883	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	103600bf1 116550eu1 2590e1 90650h1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 12950c1

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	-4	8	0	2	10	+	6	12	-8	6	4	-6	-8	0	-2	-16	-14	-12	16

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Quadratic twists for elliptic curve 12950c1

-4	-3	5	-7
103600bf1	116550eu1	2590e1	90650h1

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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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