Elliptic curve isogeny class with LMFDB label 40656.cf (Cremona label 40656dj)

• Label: 40656.cf
• Number of curves: $4$
• Conductor: $40656$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 40656.cf have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 40656.cf do not have complex multiplication.

Modular form 40656.2.a.cf

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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 40656.cf

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
40656.cf1	40656dj4	\([0, 1, 0, -438544, -111881068]\)	\(1285429208617/614922\)	\(4462067028959232\)	\([2]\)	\(368640\)	\(1.9578\)
40656.cf2	40656dj3	\([0, 1, 0, -244944, 45802260]\)	\(223980311017/4278582\)	\(31046733850632192\)	\([4]\)	\(368640\)	\(1.9578\)
40656.cf3	40656dj2	\([0, 1, 0, -31984, -1134124]\)	\(498677257/213444\)	\(1548816654680064\)	\([2, 2]\)	\(184320\)	\(1.6112\)
40656.cf4	40656dj1	\([0, 1, 0, 6736, -127404]\)	\(4657463/3696\)	\(-26819336011776\)	\([2]\)	\(92160\)	\(1.2646\)	\(\Gamma_0(N)\)-optimal