Cremona's table of elliptic curves

62400 = 2⁶ · 3 · 5² · 13

Field	Data	Notes
Atkin-Lehner	2- 3+ 5+ 13-	Signs for the Atkin-Lehner involutions
Class	62400ex	Isogeny class
Conductor	62400	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	316368000000 = 210 · 32 · 56 · 133	Discriminant
Eigenvalues	2- 3+ 5+  2  0 13-  6  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-73333,7668037]	[a1,a2,a3,a4,a6]
Generators	[-143:3900:1]	Generators of the group modulo torsion
j	2725888000000/19773	j-invariant
L	6.4582071624471	L(r)(E,1)/r!
Ω	0.86537504126722	Real period
R	1.2438166218051	Regulator
r	1	Rank of the group of rational points
S	0.99999999998552	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	62400cz3 15600ce3 2496ba3	Quadratic twists by: -4 8 5

Hecke Eigenvalues for elliptic curve 62400ex3

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

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Quadratic twists for elliptic curve 62400ex3

-4	8	5
62400cz3	15600ce3	2496ba3

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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