Cremona's table of elliptic curves

37518 = 2 · 3 · 13² · 37

Field	Data	Notes
Atkin-Lehner	2+ 3- 13- 37+	Signs for the Atkin-Lehner involutions
Class	37518i	Isogeny class
Conductor	37518	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	164736	Modular degree for the optimal curve
Δ	226003090637376 = 26 · 32 · 139 · 37	Discriminant
Eigenvalues	2+ 3-  2 -4  0 13- -4  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-19270,731096]	[a1,a2,a3,a4,a6]
Generators	[-80:1367:1]	Generators of the group modulo torsion
j	74618461/21312	j-invariant
L	4.8925049567151	L(r)(E,1)/r!
Ω	0.52015244068068	Real period
R	4.7029529942354	Regulator
r	1	Rank of the group of rational points
S	0.99999999999977	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	112554ba1 37518u1	Quadratic twists by: -3 13

Hecke Eigenvalues for elliptic curve 37518i1

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	-4	0	-	-4	4	-4	-6	0	+	6	12	2	6	-4	0	2	-2	-4	6	-4	-6	6

---

Quadratic twists for elliptic curve 37518i1

-3	13
112554ba1	37518u1

---

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