Elliptic curve isogeny class with Cremona label 388416fl (LMFDB label 388416.fl)

• Label: 388416fl
• Number of curves: $4$
• Conductor: $388416$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 388416fl have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(7\)	\(1 - T\)
\(17\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 388416fl do not have complex multiplication.

Modular form 388416.2.a.fl

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 388416fl

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
388416.fl4	388416fl1	\([0, 1, 0, -816880849, 9069630529871]\)	\(-152435594466395827792/1646846627220711\)	\(-651278321204546600821702656\)	\([2]\)	\(159252480\)	\(3.9610\)	\(\Gamma_0(N)\)-optimal
388416.fl3	388416fl2	\([0, 1, 0, -13103796769, 577351778745791]\)	\(157304700372188331121828/18069292138401\)	\(28583446824341450730307584\)	\([2, 2]\)	\(318504960\)	\(4.3076\)
388416.fl1	388416fl3	\([0, 1, 0, -209660742529, 36950725639692767]\)	\(322159999717985454060440834/4250799\)	\(13448505480659730432\)	\([2]\)	\(637009920\)	\(4.6542\)
388416.fl2	388416fl4	\([0, 1, 0, -13137505729, 574231994272415]\)	\(79260902459030376659234/842751810121431609\)	\(2666263998192805981849979584512\)	\([2]\)	\(637009920\)	\(4.6542\)