Elliptic curve isogeny class with Cremona label 51984cw (LMFDB label 51984.i)

• Label: 51984cw
• Number of curves: $3$
• Conductor: $51984$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 51984cw have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(19\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 4 T + 5 T^{2}\)	1.5.ae
\(7\)	\( 1 - 3 T + 7 T^{2}\)	1.7.ad
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 - 5 T + 13 T^{2}\)	1.13.af
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 - 8 T + 29 T^{2}\)	1.29.ai
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 51984cw do not have complex multiplication.

Modular form 51984.2.a.cw

Isogeny matrix

The \((i,j)\)-th 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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 51984cw

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
51984.i3	51984cw1	\([0, 0, 0, 34656, 109744]\)	\(32768/19\)	\(-2669086710706176\)	\([]\)	\(207360\)	\(1.6495\)	\(\Gamma_0(N)\)-optimal
51984.i2	51984cw2	\([0, 0, 0, -485184, 138387184]\)	\(-89915392/6859\)	\(-963540302564929536\)	\([]\)	\(622080\)	\(2.1988\)
51984.i1	51984cw3	\([0, 0, 0, -39993024, 97347427504]\)	\(-50357871050752/19\)	\(-2669086710706176\)	\([]\)	\(1866240\)	\(2.7481\)