Cremona's table of elliptic curves

825 = 3 · 5² · 11

Field	Data	Notes
Atkin-Lehner	3+ 5+ 11+	Signs for the Atkin-Lehner involutions
Class	825a	Isogeny class
Conductor	825	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	-132867075 = -1 · 3 · 52 · 116	Discriminant
Eigenvalues	0 3+ 5+  1 11+  1  6 -7	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,127,38]	[a1,a2,a3,a4,a6]
Generators	[76:665:1]	Generators of the group modulo torsion
j	8990228480/5314683	j-invariant
L	1.8040304299532	L(r)(E,1)/r!
Ω	1.1249255113251	Real period
R	0.80184439404708	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	13200ch2 52800cs2 2475i2 825c2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 825a2

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	+	+	1	+	1	6	-7	-6	-6	-7	-2	-6	1	0	6	0	5	-5	-12	-14	-4	6	6	-17

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Quadratic twists for elliptic curve 825a2

-4	8	-3	5	-7	-11
13200ch2	52800cs2	2475i2	825c2	40425ca2	9075f2

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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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