Elliptic curve isogeny class with LMFDB label 296450.ib (Cremona label 296450ib)

• Label: 296450.ib
• Number of curves: $2$
• Conductor: $296450$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 296450.ib have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(5\)	\(1\)
\(7\)	\(1\)
\(11\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 - 4 T + 17 T^{2}\)	1.17.ae
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 - 4 T + 29 T^{2}\)	1.29.ae
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 296450.ib do not have complex multiplication.

Modular form 296450.2.a.ib

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 296450.ib

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
296450.ib1	296450ib2	\([1, -1, 1, -45458755, 117716628747]\)	\(9300746727/24200\)	\(27031731377605521875000\)	\([2]\)	\(30965760\)	\(3.1798\)
296450.ib2	296450ib1	\([1, -1, 1, -3955755, 263138747]\)	\(6128487/3520\)	\(3931888200378985000000\)	\([2]\)	\(15482880\)	\(2.8333\)	\(\Gamma_0(N)\)-optimal