Elliptic curve isogeny class with LMFDB label 68450.bd (Cremona label 68450bm)

• Label: 68450.bd
• Number of curves: $1$
• Conductor: $68450$
• CM: no
• Rank: $1$

Rank

The elliptic curve 68450.bd1 has rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(5\)	\(1\)
\(37\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + T + 3 T^{2}\)	1.3.b
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(19\)	\( 1 - 3 T + 19 T^{2}\)	1.19.ad
\(23\)	\( 1 + 2 T + 23 T^{2}\)	1.23.c
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 68450.bd do not have complex multiplication.

Modular form 68450.2.a.bd

Elliptic curves in class 68450.bd

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
68450.bd1	68450bm1	\([1, 1, 1, -103388, -80763969]\)	\(-121945/2738\)	\(-2744124573375781250\)	\([]\)	\(1313280\)	\(2.2188\)	\(\Gamma_0(N)\)-optimal