Elliptic curve isogeny class with Cremona label 38720bt (LMFDB label 38720.bt)

• Label: 38720bt
• Number of curves: $4$
• Conductor: $38720$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 38720bt have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 38720bt do not have complex multiplication.

Modular form 38720.2.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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 38720bt

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
38720.bt3	38720bt1	\([0, 0, 0, -2440328, 1467305048]\)	\(885956203616256/15125\)	\(27437936768000\)	\([2]\)	\(552960\)	\(2.1205\)	\(\Gamma_0(N)\)-optimal
38720.bt2	38720bt2	\([0, 0, 0, -2442748, 1464249072]\)	\(55537159171536/228765625\)	\(6639980697856000000\)	\([2, 2]\)	\(1105920\)	\(2.4671\)
38720.bt4	38720bt3	\([0, 0, 0, -1271468, 2871190608]\)	\(-1957960715364/29541015625\)	\(-3429742096000000000000\)	\([2]\)	\(2211840\)	\(2.8136\)
38720.bt1	38720bt4	\([0, 0, 0, -3652748, -138274928]\)	\(46424454082884/26794860125\)	\(3110910636713910272000\)	\([2]\)	\(2211840\)	\(2.8136\)