Elliptic curve isogeny class with Cremona label 148137b (LMFDB label 148137.d)

• Label: 148137b
• Number of curves: $2$
• Conductor: $148137$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 148137b have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1 + T\)
\(11\)	\(1 - T\)
\(67\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + T + 2 T^{2}\)	1.2.b
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 148137b do not have complex multiplication.

Modular form 148137.2.a.b

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 148137b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
148137.d2	148137b1	\([1, 0, 0, -473683, 109469936]\)	\(129938649625/17924577\)	\(1621428236483667513\)	\([2]\)	\(1615680\)	\(2.2208\)	\(\Gamma_0(N)\)-optimal
148137.d1	148137b2	\([1, 0, 0, -1977498, -960344055]\)	\(9454162623625/1068251283\)	\(96632282810138572827\)	\([2]\)	\(3231360\)	\(2.5674\)