Elliptic curve isogeny class with Cremona label 51984c (LMFDB label 51984.bm)

• Label: 51984c
• Number of curves: $2$
• Conductor: $51984$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 51984c 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.e
\(7\)	\( 1 - 3 T + 7 T^{2}\)	1.7.ad
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 + 5 T + 13 T^{2}\)	1.13.f
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 - 8 T + 29 T^{2}\)	1.29.ai
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 51984.2.a.c

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 51984c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
51984.bm1	51984c1	\([0, 0, 0, -5415, -96026]\)	\(54000/19\)	\(6178441459968\)	\([2]\)	\(46080\)	\(1.1556\)	\(\Gamma_0(N)\)-optimal
51984.bm2	51984c2	\([0, 0, 0, 16245, -672182]\)	\(364500/361\)	\(-469561550957568\)	\([2]\)	\(92160\)	\(1.5022\)