Elliptic curve isogeny class with Cremona label 17600m (LMFDB label 17600.bm)

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

Rank

The elliptic curves in class 17600m 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 \(\mathbb{F}_p\)
\(3\)	\( 1 + 2 T + 3 T^{2}\)	1.3.c
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 2 T + 23 T^{2}\)	1.23.c
\(29\)	\( 1 - 10 T + 29 T^{2}\)	1.29.ak
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 17600.2.a.m

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 17600m

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
17600.bm3	17600m1	\([0, 0, 0, -504200, 137801000]\)	\(885956203616256/15125\)	\(242000000000\)	\([2]\)	\(110592\)	\(1.7263\)	\(\Gamma_0(N)\)-optimal
17600.bm2	17600m2	\([0, 0, 0, -504700, 137514000]\)	\(55537159171536/228765625\)	\(58564000000000000\)	\([2, 2]\)	\(221184\)	\(2.0728\)
17600.bm1	17600m3	\([0, 0, 0, -754700, -12986000]\)	\(46424454082884/26794860125\)	\(27437936768000000000\)	\([2]\)	\(442368\)	\(2.4194\)
17600.bm4	17600m4	\([0, 0, 0, -262700, 269646000]\)	\(-1957960715364/29541015625\)	\(-30250000000000000000\)	\([2]\)	\(442368\)	\(2.4194\)