Elliptic curve isogeny class with Cremona label 337896bh (LMFDB label 337896.bh)

• Label: 337896bh
• Number of curves: $2$
• Conductor: $337896$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 337896bh have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(13\)	\(1 - T\)
\(19\)	\(1\)

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.ae
\(11\)	\( 1 - 6 T + 11 T^{2}\)	1.11.ag
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 337896bh do not have complex multiplication.

Modular form 337896.2.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 Cremona numbering.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 337896bh

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
337896.bh1	337896bh1	\([0, 0, 0, -4819350, -4028763971]\)	\(22559008000000/277116957\)	\(152066033560862420688\)	\([2]\)	\(12902400\)	\(2.6828\)	\(\Gamma_0(N)\)-optimal
337896.bh2	337896bh2	\([0, 0, 0, -871815, -10434034262]\)	\(-8346562000/5351892507\)	\(-46989030156452828990208\)	\([2]\)	\(25804800\)	\(3.0294\)