Cremona's table of elliptic curves

715 = 5 · 11 · 13

Field	Data	Notes
Atkin-Lehner	5- 11+ 13-	Signs for the Atkin-Lehner involutions
Class	715a	Isogeny class
Conductor	715	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	48	Modular degree for the optimal curve
Δ	-17875 = -1 · 53 · 11 · 13	Discriminant
Eigenvalues	0 -2 5-  2 11+ 13- -3  5	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-5,6]	[a1,a2,a3,a4,a6]
Generators	[-2:3:1]	Generators of the group modulo torsion
j	-16777216/17875	j-invariant
L	1.5787090658482	L(r)(E,1)/r!
Ω	3.5289602069209	Real period
R	1.3420744128132	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	11440v1 45760h1 6435i1 3575b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 715a1

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	+	-	-3	5	-6	-6	-10	-1	-9	-7	9	-12	0	-4	5	0	2	-10	6	0	17

---

Quadratic twists for elliptic curve 715a1

-4	8	-3	5	-7	-11	13
11440v1	45760h1	6435i1	3575b1	35035a1	7865d1	9295b1

---

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