Cremona's table of elliptic curves

97682 = 2 · 13² · 17²

Field	Data	Notes
Atkin-Lehner	2+ 13+ 17+	Signs for the Atkin-Lehner involutions
Class	97682b	Isogeny class
Conductor	97682	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	4644864	Modular degree for the optimal curve
Δ	3.8694309598703E+20	Discriminant
Eigenvalues	2+  0  2  4 -2 13+ 17+  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-4575791,3647782425]	[a1,a2,a3,a4,a6]
Generators	[5086825:-24090490:4913]	Generators of the group modulo torsion
j	90942871473/3321188	j-invariant
L	5.9466072906632	L(r)(E,1)/r!
Ω	0.16778180873059	Real period
R	8.8606258114513	Regulator
r	1	Rank of the group of rational points
S	0.99999999834227	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	7514e1 5746a1	Quadratic twists by: 13 17

Hecke Eigenvalues for elliptic curve 97682b1

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	4	-2	+	+	0	-2	-8	-8	-6	12	4	8	-6	4	8	8	-8	8	10	0	-6	-16

---

Quadratic twists for elliptic curve 97682b1

13	17
7514e1	5746a1

---

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