Elliptic curve isogeny class with LMFDB label 38025.ck (Cremona label 38025cs)

• Label: 38025.ck
• Number of curves: $2$
• Conductor: $38025$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 38025.ck have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1\)
\(5\)	\(1\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 - T + 2 T^{2}\)	1.2.ab
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 + 2 T + 11 T^{2}\)	1.11.c
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 + 6 T + 19 T^{2}\)	1.19.g
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 38025.ck do not have complex multiplication.

Modular form 38025.2.a.ck

Isogeny matrix

The \((i,j)\)-th 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.

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

Isogeny graph

The vertices are labelled with LMFDB labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 38025.ck

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
38025.ck1	38025cs2	\([1, -1, 0, -13233492, 18531699291]\)	\(16974593\)	\(15098984458822265625\)	\([2]\)	\(1198080\)	\(2.7423\)
38025.ck2	38025cs1	\([1, -1, 0, -875367, 254032416]\)	\(4913\)	\(15098984458822265625\)	\([2]\)	\(599040\)	\(2.3957\)	\(\Gamma_0(N)\)-optimal