Elliptic curve isogeny class with LMFDB label 295659.bh (Cremona label 295659bh)

• Label: 295659.bh
• Number of curves: $4$
• Conductor: $295659$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 295659.bh have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1\)
\(7\)	\(1 - T\)
\(13\)	\(1 + T\)
\(19\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 - T + 2 T^{2}\)	1.2.ab
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 295659.bh do not have complex multiplication.

Modular form 295659.2.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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 295659.bh

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
295659.bh1	295659bh4	\([1, -1, 0, -3231198, -1736800461]\)	\(108784086144553/24922699893\)	\(854760062182932444357\)	\([2]\)	\(13271040\)	\(2.7289\)
295659.bh2	295659bh2	\([1, -1, 0, -1070613, 403475040]\)	\(3957057343513/242144721\)	\(8304703650400322529\)	\([2, 2]\)	\(6635520\)	\(2.3823\)
295659.bh3	295659bh1	\([1, -1, 0, -1054368, 416974635]\)	\(3779648905033/15561\)	\(533687015641689\)	\([2]\)	\(3317760\)	\(2.0357\)	\(\Gamma_0(N)\)-optimal
295659.bh4	295659bh3	\([1, -1, 0, 830052, 1679581521]\)	\(1844124275447/36609384357\)	\(-1255571819418216283893\)	\([2]\)	\(13271040\)	\(2.7289\)