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	8	Product of Tamagawa factors cp
Δ	18252 = 22 · 33 · 132	Discriminant
Eigenvalues	2+ 3+ -2 -2 -4 13+  0 -6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-63,209]	[a1,a2,a3,a4,a6]
Generators	[8:-17:1]	Generators of the group modulo torsion
j	1033364331/676	j-invariant
L	1.063655309114	L(r)(E,1)/r!
Ω	3.8376981201778	Real period
R	0.13857985644071	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	1872k2 7488f2 234b2 5850be2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 234c2

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

---

Quadratic twists for elliptic curve 234c2

-4	8	-3	5	-7	-11	13	17	-19	-23
1872k2	7488f2	234b2	5850be2	11466g2	28314bi2	3042i2	67626a2	84474bo2	123786b2

---

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
Back to Tables and computations