Cremona's table of elliptic curves

650 = 2 · 5² · 13

Field	Data	Notes
Atkin-Lehner	2- 5- 13-	Signs for the Atkin-Lehner involutions
Class	650m	Isogeny class
Conductor	650	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	600	Modular degree for the optimal curve
Δ	-132031250 = -1 · 2 · 58 · 132	Discriminant
Eigenvalues	2-  3 5-  0 -3 13- -7  1	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-555,5197]	[a1,a2,a3,a4,a6]
j	-48317985/338	j-invariant
L	3.7171165881619	L(r)(E,1)/r!
Ω	1.858558294081	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	5200bk1 20800br1 5850w1 650c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 650m1

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
-	3	-	0	-3	-	-7	1	-4	4	-10	12	-5	12	-4	6	-4	4	-5	0	-11	4	15	-11	-2

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Quadratic twists for elliptic curve 650m1

-4	8	-3	5	-7	-11	13
5200bk1	20800br1	5850w1	650c1	31850ck1	78650bg1	8450l1

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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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