Elliptic curve isogeny class with Cremona label 145200fq (LMFDB label 145200.dd)

• Label: 145200fq
• Number of curves: $4$
• Conductor: $145200$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 145200fq have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 5 T + 7 T^{2}\)	1.7.af
\(13\)	\( 1 - T + 13 T^{2}\)	1.13.ab
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(19\)	\( 1 + 5 T + 19 T^{2}\)	1.19.f
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 - 9 T + 29 T^{2}\)	1.29.aj
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 145200fq do not have complex multiplication.

Modular form 145200.2.a.fq

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 145200fq

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
145200.dd3	145200fq1	\([0, -1, 0, -67446408, -213176444688]\)	\(299270638153369/1069200\)	\(121225793356800000000\)	\([2]\)	\(11059200\)	\(3.0717\)	\(\Gamma_0(N)\)-optimal
145200.dd2	145200fq2	\([0, -1, 0, -68414408, -206741180688]\)	\(312341975961049/17862322500\)	\(2025228410267040000000000\)	\([2, 2]\)	\(22118400\)	\(3.4182\)
145200.dd1	145200fq3	\([0, -1, 0, -201514408, 842086819312]\)	\(7981893677157049/1917731420550\)	\(217432204359742627200000000\)	\([2]\)	\(44236800\)	\(3.7648\)
145200.dd4	145200fq4	\([0, -1, 0, 49197592, -843727772688]\)	\(116149984977671/2779502343750\)	\(-315139708902150000000000000\)	\([2]\)	\(44236800\)	\(3.7648\)