Elliptic curve isogeny class with LMFDB label 297920.bh (Cremona label 297920bh)

• Label: 297920.bh
• Number of curves: $2$
• Conductor: $297920$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 297920.bh have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1 - T\)
\(7\)	\(1\)
\(19\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 2 T + 3 T^{2}\)	1.3.c
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(13\)	\( 1 + 7 T + 13 T^{2}\)	1.13.h
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(23\)	\( 1 + 9 T + 23 T^{2}\)	1.23.j
\(29\)	\( 1 - 9 T + 29 T^{2}\)	1.29.aj
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 297920.bh do not have complex multiplication.

Modular form 297920.2.a.bh

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 297920.bh

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
297920.bh1	297920bh1	\([0, 1, 0, -5127425, -4678934177]\)	\(-483385461758641/26693632000\)	\(-823257756118024192000\)	\([]\)	\(19906560\)	\(2.7712\)	\(\Gamma_0(N)\)-optimal
297920.bh2	297920bh2	\([0, 1, 0, 27486975, -9208321697]\)	\(74469146542554959/44285662466080\)	\(-1365813206311723576852480\)	\([]\)	\(59719680\)	\(3.3205\)