Cremona's table of elliptic curves

122304 = 2⁶ · 3 · 7² · 13

Field	Data	Notes
Atkin-Lehner	2+ 3- 7- 13+	Signs for the Atkin-Lehner involutions
Class	122304db	Isogeny class
Conductor	122304	Conductor
∏ cp	68	Product of Tamagawa factors cp
deg	2350080	Modular degree for the optimal curve
Δ	-8970858679158964224 = -1 · 223 · 317 · 72 · 132	Discriminant
Eigenvalues	2+ 3- -1 7-  1 13+  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-90561,-144515169]	[a1,a2,a3,a4,a6]
Generators	[717:12636:1]	Generators of the group modulo torsion
j	-6394640503489/698390001504	j-invariant
L	7.9626677974416	L(r)(E,1)/r!
Ω	0.10248278364628	Real period
R	1.1426119716613	Regulator
r	1	Rank of the group of rational points
S	1.0000000030856	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	122304fc1 3822u1 122304d1	Quadratic twists by: -4 8 -7

Hecke Eigenvalues for elliptic curve 122304db1

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	+	6	-4	-6	-3	11	-4	-12	8	8	5	-5	12	-16	6	10	7	-17	12	-13

---

Quadratic twists for elliptic curve 122304db1

-4	8	-7
122304fc1	3822u1	122304d1

---

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