Elliptic curve isogeny class with LMFDB label 72128.bf (Cremona label 72128bv)

• Label: 72128.bf
• Number of curves: $2$
• Conductor: $72128$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 72128.bf have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(7\)	\(1\)
\(23\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 - 4 T + 17 T^{2}\)	1.17.ae
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 72128.bf do not have complex multiplication.

Modular form 72128.2.a.bf

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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 72128.bf

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
72128.bf1	72128bv2	\([0, 0, 0, -191884, 32351760]\)	\(50668941906/1127\)	\(17378891923456\)	\([2]\)	\(196608\)	\(1.6555\)
72128.bf2	72128bv1	\([0, 0, 0, -11564, 543312]\)	\(-22180932/3703\)	\(-28551036731392\)	\([2]\)	\(98304\)	\(1.3089\)	\(\Gamma_0(N)\)-optimal