Elliptic curve isogeny class with LMFDB label 328510.bp (Cremona label 328510bp)

• Label: 328510.bp
• Number of curves: $4$
• Conductor: $328510$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 328510.bp have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(5\)	\(1 + T\)
\(7\)	\(1 - T\)
\(13\)	\(1 - T\)
\(19\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 328510.bp do not have complex multiplication.

Modular form 328510.2.a.bp

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 328510.bp

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
328510.bp1	328510bp3	\([1, -1, 1, -39363508, 95065018231]\)	\(143378317900125424089/4976562500000\)	\(234126767164062500000\)	\([2]\)	\(26542080\)	\(2.9992\)
328510.bp2	328510bp2	\([1, -1, 1, -2570388, 1345582967]\)	\(39920686684059609/6492304000000\)	\(305436161399824000000\)	\([2, 2]\)	\(13271040\)	\(2.6526\)
328510.bp3	328510bp1	\([1, -1, 1, -722068, -215877769]\)	\(884984855328729/83492864000\)	\(3927995344093184000\)	\([2]\)	\(6635520\)	\(2.3060\)	\(\Gamma_0(N)\)-optimal
328510.bp4	328510bp4	\([1, -1, 1, 4649612, 7537454967]\)	\(236293804275620391/658593925444000\)	\(-30984131443761296164000\)	\([2]\)	\(26542080\)	\(2.9992\)