Elliptic curve isogeny class with LMFDB label 145200.fa (Cremona label 145200gl)

• Label: 145200.fa
• Number of curves: $4$
• Conductor: $145200$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 145200.fa have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 145200.fa do not have complex multiplication.

Modular form 145200.2.a.fa

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 145200.fa

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
145200.fa1	145200gl4	\([0, -1, 0, -17037808, -27063101888]\)	\(4824238966273/66\)	\(7483073664000000\)	\([2]\)	\(5898240\)	\(2.6019\)
145200.fa2	145200gl2	\([0, -1, 0, -1065808, -421805888]\)	\(1180932193/4356\)	\(493882861824000000\)	\([2, 2]\)	\(2949120\)	\(2.2553\)
145200.fa3	145200gl3	\([0, -1, 0, -581808, -807069888]\)	\(-192100033/2371842\)	\(-268919218263168000000\)	\([2]\)	\(5898240\)	\(2.6019\)
145200.fa4	145200gl1	\([0, -1, 0, -97808, 242112]\)	\(912673/528\)	\(59864589312000000\)	\([2]\)	\(1474560\)	\(1.9087\)	\(\Gamma_0(N)\)-optimal