Cremona's table of elliptic curves

1925 = 5² · 7 · 11

Field	Data	Notes
Atkin-Lehner	5+ 7+ 11+	Signs for the Atkin-Lehner involutions
Class	1925c	Isogeny class
Conductor	1925	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	768	Modular degree for the optimal curve
Δ	-330859375 = -1 · 58 · 7 · 112	Discriminant
Eigenvalues	1  2 5+ 7+ 11+ -4  4 -8	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,0,875]	[a1,a2,a3,a4,a6]
Generators	[118:469:8]	Generators of the group modulo torsion
j	-1/21175	j-invariant
L	4.5075282800805	L(r)(E,1)/r!
Ω	1.3609193082207	Real period
R	3.3121201623437	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	30800cb1 123200be1 17325t1 385b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1925c1

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	2	+	+	+	-4	4	-8	0	-6	-6	6	0	4	6	-10	-14	12	-12	-12	8	8	16	-14	2

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Quadratic twists for elliptic curve 1925c1

-4	8	-3	5	-7	-11
30800cb1	123200be1	17325t1	385b1	13475d1	21175v1

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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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