Elliptic curve isogeny class with Cremona label 228888m (LMFDB label 228888.bh)

• Label: 228888m
• Number of curves: $2$
• Conductor: $228888$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 228888m have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(11\)	\(1 - T\)
\(17\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 228888m do not have complex multiplication.

Modular form 228888.2.a.m

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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 228888m

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
228888.bh1	228888m1	\([0, 0, 0, -515401155, 4503666202542]\)	\(840308702533978500/594473\)	\(10711570429874045952\)	\([2]\)	\(30965760\)	\(3.3983\)	\(\Gamma_0(N)\)-optimal
228888.bh2	228888m2	\([0, 0, 0, -515297115, 4505575315734]\)	\(-419899962807227250/353398147729\)	\(-12735478816317027438446592\)	\([2]\)	\(61931520\)	\(3.7449\)