Cremona's table of elliptic curves

738 = 2 · 3² · 41

Field	Data	Notes
Atkin-Lehner	2+ 3+ 41+	Signs for the Atkin-Lehner involutions
Class	738a	Isogeny class
Conductor	738	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	240	Modular degree for the optimal curve
Δ	-25824096 = -1 · 25 · 39 · 41	Discriminant
Eigenvalues	2+ 3+  1 -4  4 -5  1 -3	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,66,116]	[a1,a2,a3,a4,a6]
Generators	[1:13:1]	Generators of the group modulo torsion
j	1601613/1312	j-invariant
L	1.6904101465164	L(r)(E,1)/r!
Ω	1.3681269309779	Real period
R	0.61778264437355	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	5904i1 23616a1 738e1 18450bc1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 738a1

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	-4	4	-5	1	-3	-8	0	7	-4	+	-6	-8	14	-7	-8	-5	-7	1	-14	-15	13	12

---

Quadratic twists for elliptic curve 738a1

-4	8	-3	5	-7	-11	13	41
5904i1	23616a1	738e1	18450bc1	36162i1	89298br1	124722bf1	30258b1

---

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