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

• Label: 254016du
• Number of curves: $4$
• Conductor: $254016$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 254016du 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 \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(11\)	\( 1 + 3 T + 11 T^{2}\)	1.11.d
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(19\)	\( 1 + T + 19 T^{2}\)	1.19.b
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 254016.2.a.du

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.

\(\left(\begin{array}{rrrr} 1 & 3 & 7 & 21 \\ 3 & 1 & 21 & 7 \\ 7 & 21 & 1 & 3 \\ 21 & 7 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 254016du

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
254016.du4	254016du1	\([0, 0, 0, 8820, 49392]\)	\(3375/2\)	\(-44966148046848\)	\([]\)	\(414720\)	\(1.3091\)	\(\Gamma_0(N)\)-optimal
254016.du3	254016du2	\([0, 0, 0, -132300, 19411056]\)	\(-140625/8\)	\(-14569031967178752\)	\([]\)	\(1244160\)	\(1.8584\)
254016.du1	254016du3	\([0, 0, 0, -3378060, -2389733136]\)	\(-189613868625/128\)	\(-2877833474998272\)	\([]\)	\(2903040\)	\(2.2820\)
254016.du2	254016du4	\([0, 0, 0, -2672460, -3415901328]\)	\(-1159088625/2097152\)	\(-3819184316004106764288\)	\([]\)	\(8709120\)	\(2.8313\)