Elliptic curve isogeny class with LMFDB label 228672.bv (Cremona label 228672o)

• Label: 228672.bv
• Number of curves: $2$
• Conductor: $228672$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 228672.bv have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(397\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(17\)	\( 1 + 8 T + 17 T^{2}\)	1.17.i
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 228672.bv do not have complex multiplication.

Modular form 228672.2.a.bv

Isogeny matrix

The \((i,j)\)-th 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, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 228672.bv

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
228672.bv1	228672o1	\([0, 0, 0, -4440, -111656]\)	\(12967168000/289413\)	\(216045646848\)	\([2]\)	\(430080\)	\(0.96230\)	\(\Gamma_0(N)\)-optimal
228672.bv2	228672o2	\([0, 0, 0, 420, -342992]\)	\(686000/4255443\)	\(-50826738843648\)	\([2]\)	\(860160\)	\(1.3089\)