Elliptic curve isogeny class with LMFDB label 8450.t (Cremona label 8450p)

• Label: 8450.t
• Number of curves: $1$
• Conductor: $8450$
• CM: no
• Rank: $0$

Rank

The elliptic curve 8450.t1 has rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(5\)	\(1\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - T + 3 T^{2}\)	1.3.ab
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(11\)	\( 1 + T + 11 T^{2}\)	1.11.b
\(17\)	\( 1 - 7 T + 17 T^{2}\)	1.17.ah
\(19\)	\( 1 - 3 T + 19 T^{2}\)	1.19.ad
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 4 T + 29 T^{2}\)	1.29.e
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 8450.t do not have complex multiplication.

Modular form 8450.2.a.t

Elliptic curves in class 8450.t

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
8450.t1	8450p1	\([1, 0, 0, 50612, 48389392]\)	\(304175/21632\)	\(-1019663401250000000\)	\([]\)	\(141120\)	\(2.1351\)	\(\Gamma_0(N)\)-optimal