Elliptic curve isogeny class with Cremona label 65025bg (LMFDB label 65025.bm)

• Label: 65025bg
• Number of curves: $2$
• Conductor: $65025$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 65025bg have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1\)
\(5\)	\(1\)
\(17\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + 2 T^{2}\)	1.2.a
\(7\)	\( 1 + T + 7 T^{2}\)	1.7.b
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(19\)	\( 1 - 8 T + 19 T^{2}\)	1.19.ai
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 65025bg do not have complex multiplication.

Modular form 65025.2.a.bg

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 65025bg

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
65025.bm2	65025bg1	\([0, 0, 1, -288147450, -114964046469]\)	\(115220905984/66430125\)	\(1525463560025329881955078125\)	\([]\)	\(22560768\)	\(3.9056\)	\(\Gamma_0(N)\)-optimal
65025.bm1	65025bg2	\([0, 0, 1, -15509849700, 743457580014906]\)	\(17968412610002944/158203125\)	\(3632886469348541290283203125\)	\([]\)	\(67682304\)	\(4.4549\)