Cremona's table of elliptic curves

3172 = 2² · 13 · 61

Field	Data	Notes
Atkin-Lehner	2- 13+ 61-	Signs for the Atkin-Lehner involutions
Class	3172a	Isogeny class
Conductor	3172	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-131320690731553024 = -1 · 28 · 1310 · 612	Discriminant
Eigenvalues	2-  0  2  2 -6 13+ -2  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-103919,21685030]	[a1,a2,a3,a4,a6]
Generators	[35809270:1186887309:343000]	Generators of the group modulo torsion
j	-484806711672241488/512971448170129	j-invariant
L	3.7075954179463	L(r)(E,1)/r!
Ω	0.29893182572212	Real period
R	12.40281261117	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	12688d2 50752c2 28548d2 79300e2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3172a2

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
-	0	2	2	-6	+	-2	2	8	2	-10	-2	2	-12	6	-10	-6	-	-2	-2	10	-12	2	-18	2

---

Quadratic twists for elliptic curve 3172a2

-4	8	-3	5	13
12688d2	50752c2	28548d2	79300e2	41236d2

---

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