Elliptic curve isogeny class with LMFDB label 381150.p (Cremona label 381150p)

• Label: 381150.p
• Number of curves: $2$
• Conductor: $381150$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 381150.p have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1\)
\(5\)	\(1\)
\(7\)	\(1 + T\)
\(11\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(13\)	\( 1 + 5 T + 13 T^{2}\)	1.13.f
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 + 5 T + 19 T^{2}\)	1.19.f
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 381150.p do not have complex multiplication.

Modular form 381150.2.a.p

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 381150.p

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
381150.p1	381150p2	\([1, -1, 0, -1365727006617, 614319359347690541]\)	\(-1412658626195854329435/1927561216\)	\(-384402636879737942188800000000\)	\([]\)	\(3832012800\)	\(5.3807\)
381150.p2	381150p1	\([1, -1, 0, -16412446617, 889626289130541]\)	\(-1787281834251393315/215504279044096\)	\(-58953086601670241235763200000000\)	\([]\)	\(1277337600\)	\(4.8314\)	\(\Gamma_0(N)\)-optimal