Elliptic curve isogeny class with LMFDB label 124950.bb (Cremona label 124950t)

• Label: 124950.bb
• Number of curves: $4$
• Conductor: $124950$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 124950.bb have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1 + T\)
\(5\)	\(1\)
\(7\)	\(1\)
\(17\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 124950.bb do not have complex multiplication.

Modular form 124950.2.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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 124950.bb

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
124950.bb1	124950t4	\([1, 1, 0, -6221800, -5975999000]\)	\(14489843500598257/6246072\)	\(11481939448875000\)	\([2]\)	\(4718592\)	\(2.4242\)
124950.bb2	124950t3	\([1, 1, 0, -831800, 153999000]\)	\(34623662831857/14438442312\)	\(26541692180695125000\)	\([2]\)	\(4718592\)	\(2.4242\)
124950.bb3	124950t2	\([1, 1, 0, -390800, -92520000]\)	\(3590714269297/73410624\)	\(134948226609000000\)	\([2, 2]\)	\(2359296\)	\(2.0777\)
124950.bb4	124950t1	\([1, 1, 0, 1200, -4320000]\)	\(103823/4386816\)	\(-8064133056000000\)	\([2]\)	\(1179648\)	\(1.7311\)	\(\Gamma_0(N)\)-optimal