Cremona's table of elliptic curves

870 = 2 · 3 · 5 · 29

Field	Data	Notes
Atkin-Lehner	2+ 3- 5- 29+	Signs for the Atkin-Lehner involutions
Class	870c	Isogeny class
Conductor	870	Conductor
∏ cp	36	Product of Tamagawa factors cp
deg	288	Modular degree for the optimal curve
Δ	10570500 = 22 · 36 · 53 · 29	Discriminant
Eigenvalues	2+ 3- 5- -4  0 -4 -6  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-58,56]	[a1,a2,a3,a4,a6]
Generators	[-8:8:1]	Generators of the group modulo torsion
j	21047437081/10570500	j-invariant
L	2.0033437921929	L(r)(E,1)/r!
Ω	2.0189872281764	Real period
R	0.99225184004871	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	6960ba1 27840r1 2610l1 4350p1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 870c1

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	-4	-6	2	-6	+	-4	2	-12	8	0	-6	12	-4	14	0	2	-4	-12	-12	-10

---

Quadratic twists for elliptic curve 870c1

-4	8	-3	5	-7	-11	29
6960ba1	27840r1	2610l1	4350p1	42630a1	105270ck1	25230u1

---

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