Elliptic curve isogeny class with Cremona label 119646cd (LMFDB label 119646.br)

• Label: 119646cd
• Number of curves: $2$
• Conductor: $119646$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 119646cd have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1\)
\(17\)	\(1\)
\(23\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(11\)	\( 1 + T + 11 T^{2}\)	1.11.b
\(13\)	\( 1 + T + 13 T^{2}\)	1.13.b
\(19\)	\( 1 + 5 T + 19 T^{2}\)	1.19.f
\(29\)	\( 1 + 5 T + 29 T^{2}\)	1.29.f
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 119646cd do not have complex multiplication.

Modular form 119646.2.a.cd

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 119646cd

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
119646.br2	119646cd1	\([1, -1, 1, -3956, -206125]\)	\(-389017/828\)	\(-14569726299228\)	\([2]\)	\(331776\)	\(1.2148\)	\(\Gamma_0(N)\)-optimal
119646.br1	119646cd2	\([1, -1, 1, -81986, -9007909]\)	\(3463512697/3174\)	\(55850617480374\)	\([2]\)	\(663552\)	\(1.5614\)