Elliptic curve isogeny class with Cremona label 265650ho (LMFDB label 265650.ho)

• Label: 265650ho
• Number of curves: $4$
• Conductor: $265650$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 265650ho have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1 - T\)
\(5\)	\(1\)
\(7\)	\(1 - T\)
\(11\)	\(1 - T\)
\(23\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 265650ho do not have complex multiplication.

Modular form 265650.2.a.ho

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 265650ho

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
265650.ho4	265650ho1	\([1, 0, 0, 3412, 27792]\)	\(281140102151/183617280\)	\(-2869020000000\)	\([2]\)	\(540672\)	\(1.0793\)	\(\Gamma_0(N)\)-optimal
265650.ho3	265650ho2	\([1, 0, 0, -14588, 225792]\)	\(21973174804729/11291187600\)	\(176424806250000\)	\([2, 2]\)	\(1081344\)	\(1.4258\)
265650.ho1	265650ho3	\([1, 0, 0, -187088, 31103292]\)	\(46349134440566329/48511196580\)	\(757987446562500\)	\([2]\)	\(2162688\)	\(1.7724\)
265650.ho2	265650ho4	\([1, 0, 0, -130088, -17907708]\)	\(15581727508423609/161608177500\)	\(2525127773437500\)	\([2]\)	\(2162688\)	\(1.7724\)