Elliptic curve isogeny class with LMFDB label 388773.bb (Cremona label 388773bb)

• Label: 388773.bb
• Number of curves: $3$
• Conductor: $388773$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 388773.bb have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1\)
\(7\)	\(1 + T\)
\(11\)	\(1\)
\(17\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + 2 T^{2}\)	1.2.a
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 - 9 T + 23 T^{2}\)	1.23.aj
\(29\)	\( 1 - 9 T + 29 T^{2}\)	1.29.aj
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 388773.bb do not have complex multiplication.

Modular form 388773.2.a.bb

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 LMFDB numbering.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 388773.bb

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
388773.bb1	388773bb3	\([0, 0, 1, -133522290, 568429625288]\)	\(838870874148864000/40675641638471\)	\(12765103055589737836401957\)	\([]\)	\(64385280\)	\(3.5772\)
388773.bb2	388773bb2	\([0, 0, 1, -21464190, -38065791085]\)	\(31363160518656000/198257271191\)	\(6913158714842120489133\)	\([]\)	\(21461760\)	\(3.0279\)
388773.bb3	388773bb1	\([0, 0, 1, -21431520, -38188058076]\)	\(22759502184972288000/5831\)	\(278909249157\)	\([]\)	\(7153920\)	\(2.4786\)	\(\Gamma_0(N)\)-optimal