Cremona's table of elliptic curves

78400 = 2⁶ · 5² · 7²

Field	Data	Notes
Atkin-Lehner	2- 5+ 7-	Signs for the Atkin-Lehner involutions
Class	78400gx	Isogeny class
Conductor	78400	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	752953600000000 = 214 · 58 · 76	Discriminant
Eigenvalues	2-  0 5+ 7-  4  2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-34300,-2058000]	[a1,a2,a3,a4,a6]
Generators	[8680:808500:1]	Generators of the group modulo torsion
j	148176/25	j-invariant
L	6.8586656162156	L(r)(E,1)/r!
Ω	0.35484245125745	Real period
R	4.8321907299987	Regulator
r	1	Rank of the group of rational points
S	1.0000000002785	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	78400w2 19600i2 15680dk2 1600p2	Quadratic twists by: -4 8 5 -7

Hecke Eigenvalues for elliptic curve 78400gx2

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	+	-	4	2	2	-4	4	2	-8	6	6	8	-4	6	4	-2	-8	0	-6	0	-16	6	-14

---

Quadratic twists for elliptic curve 78400gx2

-4	8	5	-7
78400w2	19600i2	15680dk2	1600p2

---

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