Elliptic curve isogeny class with LMFDB label 17600.bz (Cremona label 17600bn)

• Label: 17600.bz
• Number of curves: $4$
• Conductor: $17600$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 17600.bz have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 17600.bz do not have complex multiplication.

Modular form 17600.2.a.bz

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 17600.bz

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
17600.bz1	17600bn3	\([0, 0, 0, -754700, 12986000]\)	\(46424454082884/26794860125\)	\(27437936768000000000\)	\([2]\)	\(442368\)	\(2.4194\)
17600.bz2	17600bn2	\([0, 0, 0, -504700, -137514000]\)	\(55537159171536/228765625\)	\(58564000000000000\)	\([2, 2]\)	\(221184\)	\(2.0728\)
17600.bz3	17600bn1	\([0, 0, 0, -504200, -137801000]\)	\(885956203616256/15125\)	\(242000000000\)	\([2]\)	\(110592\)	\(1.7263\)	\(\Gamma_0(N)\)-optimal
17600.bz4	17600bn4	\([0, 0, 0, -262700, -269646000]\)	\(-1957960715364/29541015625\)	\(-30250000000000000000\)	\([2]\)	\(442368\)	\(2.4194\)