Elliptic curve isogeny class with Cremona label 139200q (LMFDB label 139200.im)

• Label: 139200q
• Number of curves: $2$
• Conductor: $139200$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 139200q have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(5\)	\(1\)
\(29\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 3 T + 7 T^{2}\)	1.7.d
\(11\)	\( 1 + T + 11 T^{2}\)	1.11.b
\(13\)	\( 1 + 3 T + 13 T^{2}\)	1.13.d
\(17\)	\( 1 - 5 T + 17 T^{2}\)	1.17.af
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 139200q do not have complex multiplication.

Modular form 139200.2.a.q

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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 139200q

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
139200.im1	139200q1	\([0, 1, 0, -2793, 55893]\)	\(-301302001664/87\)	\(-696000\)	\([]\)	\(72960\)	\(0.48787\)	\(\Gamma_0(N)\)-optimal
139200.im2	139200q2	\([0, 1, 0, 4607, 280493]\)	\(1351431663616/4984209207\)	\(-39873673656000\)	\([]\)	\(364800\)	\(1.2926\)