Elliptic curve isogeny class with LMFDB label 40768.cc (Cremona label 40768ce)

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

Rank

The elliptic curves in class 40768.cc 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
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(11\)	\( 1 + 3 T + 11 T^{2}\)	1.11.d
\(17\)	\( 1 - 7 T + 17 T^{2}\)	1.17.ah
\(19\)	\( 1 + 7 T + 19 T^{2}\)	1.19.h
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 - 5 T + 29 T^{2}\)	1.29.af
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 40768.2.a.cc

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 40768.cc

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
40768.cc1	40768ce1	\([0, 0, 0, -6860, -218736]\)	\(-56723625/13\)	\(-8182300672\)	\([]\)	\(30720\)	\(0.89368\)	\(\Gamma_0(N)\)-optimal
40768.cc2	40768ce2	\([0, 0, 0, 40180, 9045008]\)	\(11397810375/62748517\)	\(-39494402524315648\)	\([]\)	\(215040\)	\(1.8666\)