Cremona's table of elliptic curves

1302 = 2 · 3 · 7 · 31

Field	Data	Notes
Atkin-Lehner	2+ 3- 7- 31+	Signs for the Atkin-Lehner involutions
Class	1302f	Isogeny class
Conductor	1302	Conductor
∏ cp	140	Product of Tamagawa factors cp
deg	3360	Modular degree for the optimal curve
Δ	9968032637892 = 22 · 314 · 75 · 31	Discriminant
Eigenvalues	2+ 3- -2 7-  0 -2 -6  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-9397,-316756]	[a1,a2,a3,a4,a6]
Generators	[-68:128:1]	Generators of the group modulo torsion
j	91753989172452937/9968032637892	j-invariant
L	2.1748197878149	L(r)(E,1)/r!
Ω	0.4883220216268	Real period
R	0.12724740124616	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	10416t1 41664q1 3906s1 32550bl1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1302f1

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

---

Quadratic twists for elliptic curve 1302f1

-4	8	-3	5	-7	-31
10416t1	41664q1	3906s1	32550bl1	9114f1	40362f1

---

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