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

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

Rank

The elliptic curves in class 388416bh 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
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(19\)	\( 1 + 19 T^{2}\)	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 388416bh do not have complex multiplication.

Modular form 388416.2.a.bh

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 388416bh

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
388416.bh3	388416bh1	\([0, -1, 0, -137949, -19674435]\)	\(11745974272/357\)	\(8823922824192\)	\([2]\)	\(1474560\)	\(1.5819\)	\(\Gamma_0(N)\)-optimal
388416.bh2	388416bh2	\([0, -1, 0, -143729, -17930031]\)	\(830321872/127449\)	\(50402247171784704\)	\([2, 2]\)	\(2949120\)	\(1.9285\)
388416.bh1	388416bh3	\([0, -1, 0, -629249, 174821409]\)	\(17418812548/1753941\)	\(2774523701456338944\)	\([2]\)	\(5898240\)	\(2.2751\)
388416.bh4	388416bh4	\([0, -1, 0, 249311, -99132095]\)	\(1083360092/3306177\)	\(-5229974353589895168\)	\([2]\)	\(5898240\)	\(2.2751\)