Elliptic curve isogeny class with Cremona label 370260bt (LMFDB label 370260.bt)

• Label: 370260bt
• Number of curves: $2$
• Conductor: $370260$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 370260bt have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1 - T\)
\(11\)	\(1\)
\(17\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(19\)	\( 1 + 8 T + 19 T^{2}\)	1.19.i
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 370260bt do not have complex multiplication.

Modular form 370260.2.a.bt

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 370260bt

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
370260.bt1	370260bt1	\([0, 0, 0, -479727732, 4043933844181]\)	\(590887175978458660864/57171426328125\)	\(1181361053517067541250000\)	\([2]\)	\(75264000\)	\(3.6550\)	\(\Gamma_0(N)\)-optimal
370260.bt2	370260bt2	\([0, 0, 0, -444003087, 4671665871334]\)	\(-29279123829148431184/11573052978515625\)	\(-3826234169675001562500000000\)	\([2]\)	\(150528000\)	\(4.0016\)