Elliptic curve isogeny class with LMFDB label 281775.bq (Cremona label 281775bq)

• Label: 281775.bq
• Number of curves: $2$
• Conductor: $281775$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 281775.bq have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 - T + 2 T^{2}\)	1.2.ab
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 281775.bq do not have complex multiplication.

Modular form 281775.2.a.bq

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 LMFDB numbering.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 281775.bq

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
281775.bq1	281775bq1	\([1, 1, 0, -269890025, 32385057000]\)	\(1173340055458817/678770015625\)	\(1257717105981316566650390625\)	\([2]\)	\(105283584\)	\(3.8894\)	\(\Gamma_0(N)\)-optimal
281775.bq2	281775bq2	\([1, 1, 0, 1079342600, 260405370625]\)	\(75048384514044943/43446533203125\)	\(-80503626776796833038330078125\)	\([2]\)	\(210567168\)	\(4.2360\)