Cremona's table of elliptic curves

470 = 2 · 5 · 47

Field	Data	Notes
Atkin-Lehner	2+ 5- 47-	Signs for the Atkin-Lehner involutions
Class	470c	Isogeny class
Conductor	470	Conductor
∏ cp	14	Product of Tamagawa factors cp
deg	112	Modular degree for the optimal curve
Δ	14687500 = 22 · 57 · 47	Discriminant
Eigenvalues	2+ -1 5- -1  1 -5  0  5	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-97,281]	[a1,a2,a3,a4,a6]
Generators	[-8:29:1]	Generators of the group modulo torsion
j	102568953241/14687500	j-invariant
L	1.3213107467723	L(r)(E,1)/r!
Ω	2.1318477419218	Real period
R	0.044271144322008	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	3760l1 15040e1 4230z1 2350i1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 470c1

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	-	-1	1	-5	0	5	-6	-6	-11	-8	2	-2	-	-6	8	-5	2	12	-15	0	-1	14	6

---

Quadratic twists for elliptic curve 470c1

-4	8	-3	5	-7	-11	13	-47
3760l1	15040e1	4230z1	2350i1	23030d1	56870bb1	79430j1	22090b1

---

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