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	715b	Isogeny class
Conductor	715	Conductor
∏ cp	21	Product of Tamagawa factors cp
deg	336	Modular degree for the optimal curve
Δ	-1888046875 = -1 · 57 · 11 · 133	Discriminant
Eigenvalues	-2  0 5-  0 11+ 13- -3 -1	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,43,-2088]	[a1,a2,a3,a4,a6]
Generators	[87:812:1]	Generators of the group modulo torsion
j	8792838144/1888046875	j-invariant
L	1.2547951053403	L(r)(E,1)/r!
Ω	0.69751963330552	Real period
R	0.085663750553059	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	11440t1 45760f1 6435l1 3575c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 715b1

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
-2	0	-	0	+	-	-3	-1	-2	0	-2	1	-7	13	-9	4	-14	-10	-1	-10	-4	2	2	-14	-17

---

Quadratic twists for elliptic curve 715b1

-4	8	-3	5	-7	-11	13
11440t1	45760f1	6435l1	3575c1	35035b1	7865e1	9295d1

---

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