Elliptic curve isogeny class with LMFDB label 254016.do (Cremona label 254016do)

• Label: 254016.do
• Number of curves: $2$
• Conductor: $254016$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 254016.do have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(7\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + T + 5 T^{2}\)	1.5.b
\(11\)	\( 1 - 5 T + 11 T^{2}\)	1.11.af
\(13\)	\( 1 + 5 T + 13 T^{2}\)	1.13.f
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(19\)	\( 1 + T + 19 T^{2}\)	1.19.b
\(23\)	\( 1 + 3 T + 23 T^{2}\)	1.23.d
\(29\)	\( 1 - T + 29 T^{2}\)	1.29.ab
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 254016.do do not have complex multiplication.

Modular form 254016.2.a.do

Isogeny matrix

The \((i,j)\)-th 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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 254016.do

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
254016.do1	254016do2	\([0, 0, 0, -222348, -40355056]\)	\(1168429123449\)	\(1040449536\)	\([]\)	\(645120\)	\(1.4646\)
254016.do2	254016do1	\([0, 0, 0, -588, 5264]\)	\(21609\)	\(1040449536\)	\([]\)	\(92160\)	\(0.49163\)	\(\Gamma_0(N)\)-optimal