Elliptic curve isogeny class with Cremona label 129600fr (LMFDB label 129600.ef)

• Label: 129600fr
• Number of curves: $2$
• Conductor: $129600$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 129600fr have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - T + 7 T^{2}\)	1.7.ab
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 - 3 T + 23 T^{2}\)	1.23.ad
\(29\)	\( 1 + 3 T + 29 T^{2}\)	1.29.d
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 129600fr do not have complex multiplication.

Modular form 129600.2.a.fr

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 129600fr

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
129600.ef2	129600fr1	\([0, 0, 0, 35700, -2998000]\)	\(15166431/20480\)	\(-6794772480000000\)	\([]\)	\(663552\)	\(1.7237\)	\(\Gamma_0(N)\)-optimal
129600.ef1	129600fr2	\([0, 0, 0, -348300, 127818000]\)	\(-2146689/2000\)	\(-4353564672000000000\)	\([]\)	\(1990656\)	\(2.2730\)