Cremona's table of elliptic curves

370 = 2 · 5 · 37

Field	Data	Notes
Atkin-Lehner	2+ 5+ 37+	Signs for the Atkin-Lehner involutions
Class	370a	Isogeny class
Conductor	370	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	16	Modular degree for the optimal curve
Δ	2960 = 24 · 5 · 37	Discriminant
Eigenvalues	2+  0 5+  0 -4  2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-5,5]	[a1,a2,a3,a4,a6]
Generators	[-2:3:1]	Generators of the group modulo torsion
j	15438249/2960	j-invariant
L	1.2956210363413	L(r)(E,1)/r!
Ω	4.2831069878525	Real period
R	0.60499120849229	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	2960e1 11840o1 3330t1 1850j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 370a1

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

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Quadratic twists for elliptic curve 370a1

-4	8	-3	5	-7	-11	13	17	37
2960e1	11840o1	3330t1	1850j1	18130i1	44770m1	62530u1	106930j1	13690k1

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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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