Elliptic curve isogeny class with Cremona label 38025cr (LMFDB label 38025.cl)

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

Rank

The elliptic curves in class 38025cr 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
\(7\)	\( 1 - 3 T + 7 T^{2}\)	1.7.ad
\(11\)	\( 1 + T + 11 T^{2}\)	1.11.b
\(17\)	\( 1 - 5 T + 17 T^{2}\)	1.17.af
\(19\)	\( 1 - 8 T + 19 T^{2}\)	1.19.ai
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + T + 29 T^{2}\)	1.29.b
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 38025.2.a.cr

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 Cremona numbering.

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

Isogeny graph

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

Elliptic curves in class 38025cr

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
38025.cl2	38025cr1	\([1, -1, 0, -207, 976]\)	\(4913\)	\(200201625\)	\([2]\)	\(9216\)	\(0.30854\)	\(\Gamma_0(N)\)-optimal
38025.cl1	38025cr2	\([1, -1, 0, -3132, 68251]\)	\(16974593\)	\(200201625\)	\([2]\)	\(18432\)	\(0.65511\)