Elliptic curve isogeny class with Cremona label 68450z (LMFDB label 68450.bo)

• Label: 68450z
• Number of curves: $2$
• Conductor: $68450$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 68450z have rank \(0\).

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 \(\mathbb{F}_p\)
\(3\)	\( 1 + 2 T + 3 T^{2}\)	1.3.c
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 + 5 T + 11 T^{2}\)	1.11.f
\(13\)	\( 1 + T + 13 T^{2}\)	1.13.b
\(17\)	\( 1 - 4 T + 17 T^{2}\)	1.17.ae
\(19\)	\( 1 + 5 T + 19 T^{2}\)	1.19.f
\(23\)	\( 1 + T + 23 T^{2}\)	1.23.b
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 68450.2.a.z

Isogeny matrix

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 68450z

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
68450.bo1	68450z1	\([1, 1, 1, -1609288, 790262281]\)	\(-8398297/64\)	\(-3512479453921000000\)	\([]\)	\(2301696\)	\(2.3885\)	\(\Gamma_0(N)\)-optimal
68450.bo2	68450z2	\([1, 1, 1, 4722337, 4209339781]\)	\(212207543/262144\)	\(-14387115843260416000000\)	\([]\)	\(6905088\)	\(2.9378\)