Cremona's table of elliptic curves

235 = 5 · 47

Field	Data	Notes
Atkin-Lehner	5- 47-	Signs for the Atkin-Lehner involutions
Class	235a	Isogeny class
Conductor	235	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	12	Modular degree for the optimal curve
Δ	5875 = 53 · 47	Discriminant
Eigenvalues	-1 -1 5-  1 -3 -3 -6 -7	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-5,0]	[a1,a2,a3,a4,a6]
Generators	[-2:3:1]	Generators of the group modulo torsion
j	13997521/5875	j-invariant
L	0.96466220163723	L(r)(E,1)/r!
Ω	3.8526221203919	Real period
R	0.083463692302037	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	3760m1 15040d1 2115c1 1175b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 235a1

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
-1	-1	-	1	-3	-3	-6	-7	4	-10	3	12	-8	0	-	-4	6	5	-8	12	5	14	-17	-10	0

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Quadratic twists for elliptic curve 235a1

-4	8	-3	5	-7	-11	13	17	-19	-23	-47
3760m1	15040d1	2115c1	1175b1	11515c1	28435k1	39715a1	67915d1	84835e1	124315b1	11045a1

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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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