Cremona's table of elliptic curves

234 = 2 · 3² · 13

Field	Data	Notes
Atkin-Lehner	2+ 3+ 13+	Signs for the Atkin-Lehner involutions
Class	234c	Isogeny class
Conductor	234	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	16	Modular degree for the optimal curve
Δ	-5616 = -1 · 24 · 33 · 13	Discriminant
Eigenvalues	2+ 3+ -2 -2 -4 13+  0 -6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-3,5]	[a1,a2,a3,a4,a6]
Generators	[1:1:1]	Generators of the group modulo torsion
j	-132651/208	j-invariant
L	1.063655309114	L(r)(E,1)/r!
Ω	3.8376981201778	Real period
R	0.27715971288141	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	1872k1 7488f1 234b1 5850be1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 234c1

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

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Quadratic twists for elliptic curve 234c1

-4	8	-3	5	-7	-11	13	17	-19	-23
1872k1	7488f1	234b1	5850be1	11466g1	28314bi1	3042i1	67626a1	84474bo1	123786b1

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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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