Elliptic curve isogeny class with LMFDB label 158400.bb (Cremona label 158400cb)

• Label: 158400.bb
• Number of curves: $4$
• Conductor: $158400$
• CM: no
• Rank: $2$

Rank

The elliptic curves in class 158400.bb have rank \(2\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1\)
\(11\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 158400.bb do not have complex multiplication.

Modular form 158400.2.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.

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 158400.bb

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
158400.bb1	158400cb4	\([0, 0, 0, -1400700, -346606000]\)	\(1628514404944/664335375\)	\(123980925024000000000\)	\([2]\)	\(5308416\)	\(2.5532\)
158400.bb2	158400cb2	\([0, 0, 0, -644700, 199226000]\)	\(158792223184/16335\)	\(3048503040000000\)	\([2]\)	\(1769472\)	\(2.0039\)
158400.bb3	158400cb1	\([0, 0, 0, -37200, 3611000]\)	\(-488095744/200475\)	\(-2338340400000000\)	\([2]\)	\(884736\)	\(1.6573\)	\(\Gamma_0(N)\)-optimal
158400.bb4	158400cb3	\([0, 0, 0, 286800, -39481000]\)	\(223673040896/187171875\)	\(-2183172750000000000\)	\([2]\)	\(2654208\)	\(2.2066\)