Elliptic curve isogeny class with Cremona label 167310ea (LMFDB label 167310.d)

• Label: 167310ea
• Number of curves: $2$
• Conductor: $167310$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 167310ea have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1\)
\(5\)	\(1 + T\)
\(11\)	\(1 - T\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(17\)	\( 1 + 4 T + 17 T^{2}\)	1.17.e
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 167310ea do not have complex multiplication.

Modular form 167310.2.a.ea

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 167310ea

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
167310.d2	167310ea1	\([1, -1, 0, -19980, 28814800]\)	\(-550763061373/223556889600\)	\(-358051620622924800\)	\([2]\)	\(2580480\)	\(2.0474\)	\(\Gamma_0(N)\)-optimal
167310.d1	167310ea2	\([1, -1, 0, -1536300, 726018736]\)	\(250376968939063933/2869928820000\)	\(4596515307186660000\)	\([2]\)	\(5160960\)	\(2.3940\)