Elliptic curve isogeny class with Cremona label 369600ww (LMFDB label 369600.ww)

• Label: 369600ww
• Number of curves: $4$
• Conductor: $369600$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 369600ww have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1\)
\(7\)	\(1 - T\)
\(11\)	\(1 - T\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 369600ww do not have complex multiplication.

Modular form 369600.2.a.ww

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 369600ww

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
369600.ww3	369600ww1	\([0, 1, 0, -115633, -15173137]\)	\(667932971344/3465\)	\(887040000000\)	\([2]\)	\(1179648\)	\(1.4892\)	\(\Gamma_0(N)\)-optimal
369600.ww2	369600ww2	\([0, 1, 0, -117633, -14623137]\)	\(175798419556/12006225\)	\(12294374400000000\)	\([2, 2]\)	\(2359296\)	\(1.8357\)
369600.ww1	369600ww3	\([0, 1, 0, -369633, 68788863]\)	\(2727138195938/576489375\)	\(1180650240000000000\)	\([2]\)	\(4718592\)	\(2.1823\)
369600.ww4	369600ww4	\([0, 1, 0, 102367, -62803137]\)	\(57925453822/866412855\)	\(-1774413527040000000\)	\([2]\)	\(4718592\)	\(2.1823\)