Elliptic curve isogeny class with Cremona label 170352ch (LMFDB label 170352.es)

• Label: 170352ch
• Number of curves: $4$
• Conductor: $170352$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 170352ch have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(7\)	\(1 + T\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + T + 5 T^{2}\)	1.5.b
\(11\)	\( 1 - 5 T + 11 T^{2}\)	1.11.af
\(17\)	\( 1 - T + 17 T^{2}\)	1.17.ab
\(19\)	\( 1 + T + 19 T^{2}\)	1.19.b
\(23\)	\( 1 + 5 T + 23 T^{2}\)	1.23.f
\(29\)	\( 1 - T + 29 T^{2}\)	1.29.ab
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 170352ch do not have complex multiplication.

Modular form 170352.2.a.ch

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 170352ch

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
170352.es4	170352ch1	\([0, 0, 0, 21082581, 25291130202]\)	\(71903073502287/60782804992\)	\(-876048858487519866519552\)	\([2]\)	\(23224320\)	\(3.2818\)	\(\Gamma_0(N)\)-optimal
170352.es3	170352ch2	\([0, 0, 0, -103517739, 222583276890]\)	\(8511781274893233/3440817243136\)	\(49591722831978578225135616\)	\([2, 2]\)	\(46448640\)	\(3.6284\)
170352.es1	170352ch3	\([0, 0, 0, -1439077419, 21005227457370]\)	\(22868021811807457713/8953460393696\)	\(129044205157082741680766976\)	\([2]\)	\(92897280\)	\(3.9749\)
170352.es2	170352ch4	\([0, 0, 0, -761563179, -7933363515558]\)	\(3389174547561866673/74853681183008\)	\(1078849223272826876776808448\)	\([2]\)	\(92897280\)	\(3.9749\)