Elliptic curve isogeny class with Cremona label 147600co (LMFDB label 147600.fn)

• Label: 147600co
• Number of curves: $2$
• Conductor: $147600$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 147600co have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1\)
\(41\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 + 5 T + 17 T^{2}\)	1.17.f
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 - T + 29 T^{2}\)	1.29.ab
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 147600co do not have complex multiplication.

Modular form 147600.2.a.co

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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

Elliptic curves in class 147600co

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
147600.fn1	147600co1	\([0, 0, 0, -1634027475, -25423605008750]\)	\(10341755683137709164937/356992303104\)	\(16655832893620224000000\)	\([2]\)	\(41287680\)	\(3.7616\)	\(\Gamma_0(N)\)-optimal
147600.fn2	147600co2	\([0, 0, 0, -1631723475, -25498874384750]\)	\(-10298071306410575356297/60769798505543808\)	\(-2835275719074651906048000000\)	\([2]\)	\(82575360\)	\(4.1081\)