Elliptic curve isogeny class with Cremona label 266175dq (LMFDB label 266175.dq)

• Label: 266175dq
• Number of curves: $4$
• Conductor: $266175$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 266175dq have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1\)
\(5\)	\(1\)
\(7\)	\(1 - T\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 - T + 2 T^{2}\)	1.2.ab
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 10 T + 29 T^{2}\)	1.29.ak
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 266175dq do not have complex multiplication.

Modular form 266175.2.a.dq

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 266175dq

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
266175.dq3	266175dq1	\([1, -1, 0, -38824317, 92213050216]\)	\(117713838907729/1322517105\)	\(72712481438039561015625\)	\([2]\)	\(27869184\)	\(3.2005\)	\(\Gamma_0(N)\)-optimal
266175.dq2	266175dq2	\([1, -1, 0, -70955442, -82483876409]\)	\(718576775407009/362361861225\)	\(19922789662653383862890625\)	\([2, 2]\)	\(55738368\)	\(3.5471\)
266175.dq4	266175dq3	\([1, -1, 0, 262713933, -636708708284]\)	\(36472485598112591/24291459037755\)	\(-1335553436479491714008671875\)	\([2]\)	\(111476736\)	\(3.8937\)
266175.dq1	266175dq4	\([1, -1, 0, -918722817, -10709247922034]\)	\(1559802282754777489/1481059636875\)	\(81429208701919246669921875\)	\([2]\)	\(111476736\)	\(3.8937\)