Elliptic curve isogeny class with Cremona label 177450ih (LMFDB label 177450.ba)

• Label: 177450ih
• Number of curves: $2$
• Conductor: $177450$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 177450ih have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1 - T\)
\(5\)	\(1\)
\(7\)	\(1 + T\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 3 T + 11 T^{2}\)	1.11.d
\(17\)	\( 1 - 5 T + 17 T^{2}\)	1.17.af
\(19\)	\( 1 - 3 T + 19 T^{2}\)	1.19.ad
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 + 9 T + 29 T^{2}\)	1.29.j
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 177450ih do not have complex multiplication.

Modular form 177450.2.a.ih

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 177450ih

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
177450.ba2	177450ih1	\([1, 1, 0, -5452450, 4140664000]\)	\(865523177/142884\)	\(2959400953929164062500\)	\([2]\)	\(13178880\)	\(2.8414\)	\(\Gamma_0(N)\)-optimal
177450.ba1	177450ih2	\([1, 1, 0, -24676200, -43245879750]\)	\(80230292297/7440174\)	\(154100235386740042968750\)	\([2]\)	\(26357760\)	\(3.1880\)