Cremona's table of elliptic curves

10710 = 2 · 3² · 5 · 7 · 17

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5+ 7- 17-	Signs for the Atkin-Lehner involutions
Class	10710b	Isogeny class
Conductor	10710	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	29952	Modular degree for the optimal curve
Δ	-3149331963120 = -1 · 24 · 39 · 5 · 76 · 17	Discriminant
Eigenvalues	2+ 3+ 5+ 7- -4  0 17-  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-12300,535040]	[a1,a2,a3,a4,a6]
Generators	[61:64:1]	Generators of the group modulo torsion
j	-10456049121363/160002640	j-invariant
L	2.9796121136109	L(r)(E,1)/r!
Ω	0.80005883374833	Real period
R	0.62070687552881	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	85680cq1 10710t1 53550co1 74970k1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 10710b1

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

---

Quadratic twists for elliptic curve 10710b1

-4	-3	5	-7
85680cq1	10710t1	53550co1	74970k1

---

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