Elliptic curve isogeny class with Cremona label 381216ba (LMFDB label 381216.ba)

• Label: 381216ba
• Number of curves: $2$
• Conductor: $381216$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 381216ba have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(11\)	\(1 + T\)
\(19\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 8 T + 29 T^{2}\)	1.29.ai
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 381216ba do not have complex multiplication.

Modular form 381216.2.a.ba

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 381216ba

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
381216.ba2	381216ba1	\([0, 1, 0, 2046, 234396]\)	\(314432/8019\)	\(-24144698863296\)	\([2]\)	\(684288\)	\(1.2481\)	\(\Gamma_0(N)\)-optimal
381216.ba1	381216ba2	\([0, 1, 0, -46689, 3675087]\)	\(58411072/3267\)	\(629550666657792\)	\([2]\)	\(1368576\)	\(1.5947\)