Elliptic curve isogeny class with Cremona label 265200cw (LMFDB label 265200.cw)

• Label: 265200cw
• Number of curves: $2$
• Conductor: $265200$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 265200cw have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(5\)	\(1\)
\(13\)	\(1 - T\)
\(17\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(19\)	\( 1 + 6 T + 19 T^{2}\)	1.19.g
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 265200cw do not have complex multiplication.

Modular form 265200.2.a.cw

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 265200cw

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
265200.cw1	265200cw1	\([0, -1, 0, -61551633, 123448272012]\)	\(103157889656032577929216/33372791198022770325\)	\(8343197799505692581250000\)	\([2]\)	\(47185920\)	\(3.4854\)	\(\Gamma_0(N)\)-optimal
265200.cw2	265200cw2	\([0, -1, 0, 175464492, 843977292012]\)	\(149359017613560984774704/163373427681970325625\)	\(-653493710727881302500000000\)	\([2]\)	\(94371840\)	\(3.8319\)