Elliptic curve isogeny class with Cremona label 381480bk (LMFDB label 381480.bk)

• Label: 381480bk
• Number of curves: $4$
• Conductor: $381480$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 381480bk have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 381480bk do not have complex multiplication.

Modular form 381480.2.a.bk

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 381480bk

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
381480.bk4	381480bk1	\([0, 1, 0, -15991, -135070]\)	\(1171019776/658845\)	\(254446666364880\)	\([2]\)	\(1310720\)	\(1.4543\)	\(\Gamma_0(N)\)-optimal
381480.bk2	381480bk2	\([0, 1, 0, -190836, -32096736]\)	\(124386546256/245025\)	\(1514062808121600\)	\([2, 2]\)	\(2621440\)	\(1.8009\)
381480.bk3	381480bk3	\([0, 1, 0, -127256, -53764800]\)	\(-9220796644/45106875\)	\(-1114900795071360000\)	\([2]\)	\(5242880\)	\(2.1474\)
381480.bk1	381480bk4	\([0, 1, 0, -3051936, -2053177776]\)	\(127191074376964/495\)	\(12234850974720\)	\([2]\)	\(5242880\)	\(2.1474\)