Elliptic curve isogeny class with LMFDB label 51408.bo (Cremona label 51408t)

• Label: 51408.bo
• Number of curves: $3$
• Conductor: $51408$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 51408.bo have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(7\)	\(1 + T\)
\(17\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 + 9 T + 23 T^{2}\)	1.23.j
\(29\)	\( 1 + 9 T + 29 T^{2}\)	1.29.j
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 51408.bo do not have complex multiplication.

Modular form 51408.2.a.bo

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 LMFDB numbering.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 51408.bo

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
51408.bo1	51408t3	\([0, 0, 0, -17655840, 27332453808]\)	\(838870874148864000/40675641638471\)	\(29514006074696590282752\)	\([]\)	\(3219264\)	\(3.0714\)
51408.bo2	51408t2	\([0, 0, 0, -2838240, -1830361104]\)	\(31363160518656000/198257271191\)	\(15983812070819647488\)	\([]\)	\(1073088\)	\(2.5221\)
51408.bo3	51408t1	\([0, 0, 0, -2833920, -1836240208]\)	\(22759502184972288000/5831\)	\(644861952\)	\([]\)	\(357696\)	\(1.9728\)	\(\Gamma_0(N)\)-optimal