Elliptic curve isogeny class with Cremona label 399c (LMFDB label 399.b)

• Label: 399c
• Number of curves: $2$
• Conductor: $399$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 399c have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1 + T\)
\(7\)	\(1 + T\)
\(19\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 - T + 2 T^{2}\)	1.2.ab
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(11\)	\( 1 + 2 T + 11 T^{2}\)	1.11.c
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 + 4 T + 17 T^{2}\)	1.17.e
\(23\)	\( 1 - 2 T + 23 T^{2}\)	1.23.ac
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 399c do not have complex multiplication.

Modular form 399.2.a.c

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 399c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
399.b2	399c1	\([1, 0, 0, -431, 3408]\)	\(8855610342769/1008273\)	\(1008273\)	\([2]\)	\(168\)	\(0.17947\)	\(\Gamma_0(N)\)-optimal
399.b1	399c2	\([1, 0, 0, -466, 2813]\)	\(11192824869409/2963890503\)	\(2963890503\)	\([2]\)	\(336\)	\(0.52604\)