Elliptic curve isogeny class with LMFDB label 145600.dr (Cremona label 145600ce)

• Label: 145600.dr
• Number of curves: $4$
• Conductor: $145600$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 145600.dr have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 145600.dr do not have complex multiplication.

Modular form 145600.2.a.dr

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 145600.dr

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
145600.dr1	145600ce3	\([0, 0, 0, -634700, 185274000]\)	\(6903498885921/374712065\)	\(1534820618240000000\)	\([2]\)	\(1572864\)	\(2.2456\)
145600.dr2	145600ce2	\([0, 0, 0, -114700, -11286000]\)	\(40743095121/10144225\)	\(41550745600000000\)	\([2, 2]\)	\(786432\)	\(1.8990\)
145600.dr3	145600ce1	\([0, 0, 0, -106700, -13414000]\)	\(32798729601/3185\)	\(13045760000000\)	\([2]\)	\(393216\)	\(1.5524\)	\(\Gamma_0(N)\)-optimal
145600.dr4	145600ce4	\([0, 0, 0, 277300, -71654000]\)	\(575722725759/874680625\)	\(-3582691840000000000\)	\([2]\)	\(1572864\)	\(2.2456\)