Elliptic curve isogeny class with Cremona label 40768cj (LMFDB label 40768.cb)

• Label: 40768cj
• Number of curves: $2$
• Conductor: $40768$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 40768cj have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(7\)	\(1\)
\(13\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 - 10 T + 29 T^{2}\)	1.29.ak
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 40768cj do not have complex multiplication.

Modular form 40768.2.a.cj

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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 40768cj

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
40768.cb1	40768cj1	\([0, 0, 0, -336140, 75026448]\)	\(-56723625/13\)	\(-962639491760128\)	\([]\)	\(215040\)	\(1.8666\)	\(\Gamma_0(N)\)-optimal
40768.cb2	40768cj2	\([0, 0, 0, 1968820, -3102437744]\)	\(11397810375/62748517\)	\(-4646476962583211671552\)	\([]\)	\(1505280\)	\(2.8396\)