Elliptic curve isogeny class with LMFDB label 159600.eg (Cremona label 159600by)

• Label: 159600.eg
• Number of curves: $4$
• Conductor: $159600$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 159600.eg have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1\)
\(7\)	\(1 + T\)
\(19\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 159600.eg do not have complex multiplication.

Modular form 159600.2.a.eg

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 159600.eg

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
159600.eg1	159600by4	\([0, 1, 0, -2511808, -1533073612]\)	\(27384399945278713/153257496\)	\(9808479744000000\)	\([2]\)	\(2359296\)	\(2.2607\)
159600.eg2	159600by2	\([0, 1, 0, -159808, -23089612]\)	\(7052482298233/499254336\)	\(31952277504000000\)	\([2, 2]\)	\(1179648\)	\(1.9142\)
159600.eg3	159600by1	\([0, 1, 0, -31808, 1742388]\)	\(55611739513/11440128\)	\(732168192000000\)	\([2]\)	\(589824\)	\(1.5676\)	\(\Gamma_0(N)\)-optimal
159600.eg4	159600by3	\([0, 1, 0, 144192, -100305612]\)	\(5180411077127/70976229912\)	\(-4542478714368000000\)	\([2]\)	\(2359296\)	\(2.2607\)