Elliptic curve isogeny class with Cremona label 254800dq (LMFDB label 254800.dq)

• Label: 254800dq
• Number of curves: $4$
• Conductor: $254800$
• CM: no
• Rank: $2$

Rank

The elliptic curves in class 254800dq have rank \(2\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1\)
\(7\)	\(1\)
\(13\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 254800dq do not have complex multiplication.

Modular form 254800.2.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 254800dq

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
254800.dq3	254800dq1	\([0, 0, 0, -1307075, 575125250]\)	\(32798729601/3185\)	\(23981572160000000\)	\([2]\)	\(2359296\)	\(2.1788\)	\(\Gamma_0(N)\)-optimal
254800.dq2	254800dq2	\([0, 0, 0, -1405075, 483887250]\)	\(40743095121/10144225\)	\(76381307329600000000\)	\([2, 2]\)	\(4718592\)	\(2.5254\)
254800.dq4	254800dq3	\([0, 0, 0, 3396925, 3072165250]\)	\(575722725759/874680625\)	\(-6585939254440000000000\)	\([2]\)	\(9437184\)	\(2.8719\)
254800.dq1	254800dq4	\([0, 0, 0, -7775075, -7943622750]\)	\(6903498885921/374712065\)	\(2821407983051840000000\)	\([2]\)	\(9437184\)	\(2.8719\)