Elliptic curve isogeny class with Cremona label 145200cp (LMFDB label 145200.je)

• Label: 145200cp
• Number of curves: $2$
• Conductor: $145200$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 145200cp have rank \(0\).

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 \(\mathbb{F}_p\)
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 - 4 T + 29 T^{2}\)	1.29.ae
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 145200.2.a.cp

Isogeny matrix

The \((i,j)\)-th 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 145200cp

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
145200.je2	145200cp1	\([0, 1, 0, -1613, -37017]\)	\(-40960/27\)	\(-306125740800\)	\([]\)	\(155520\)	\(0.90486\)	\(\Gamma_0(N)\)-optimal
145200.je1	145200cp2	\([0, 1, 0, -146813, -21700857]\)	\(-30866268160/3\)	\(-34013971200\)	\([]\)	\(466560\)	\(1.4542\)