Elliptic curve isogeny class with Cremona label 54600bb (LMFDB label 54600.cr)

• Label: 54600bb
• Number of curves: $4$
• Conductor: $54600$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 54600bb have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(5\)	\(1\)
\(7\)	\(1 - T\)
\(13\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 - 4 T + 19 T^{2}\)	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 54600bb do not have complex multiplication.

Modular form 54600.2.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 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 54600bb

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
54600.cr4	54600bb1	\([0, 1, 0, 1092, -165312]\)	\(35969456/2985255\)	\(-11941020000000\)	\([2]\)	\(122880\)	\(1.1887\)	\(\Gamma_0(N)\)-optimal
54600.cr3	54600bb2	\([0, 1, 0, -39408, -2919312]\)	\(423026849956/16769025\)	\(268304400000000\)	\([2, 2]\)	\(245760\)	\(1.5353\)
54600.cr2	54600bb3	\([0, 1, 0, -102408, 8672688]\)	\(3711757787138/1124589375\)	\(35986860000000000\)	\([2]\)	\(491520\)	\(1.8819\)
54600.cr1	54600bb4	\([0, 1, 0, -624408, -190119312]\)	\(841356017734178/1404585\)	\(44946720000000\)	\([2]\)	\(491520\)	\(1.8819\)