Elliptic curve isogeny class with Cremona label 25200bm (LMFDB label 25200.el)

• Label: 25200bm
• Number of curves: $4$
• Conductor: $25200$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 25200bm have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 25200bm do not have complex multiplication.

Modular form 25200.2.a.bm

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 25200bm

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
25200.el3	25200bm1	\([0, 0, 0, -8175, -283250]\)	\(20720464/105\)	\(306180000000\)	\([2]\)	\(24576\)	\(1.0505\)	\(\Gamma_0(N)\)-optimal
25200.el2	25200bm2	\([0, 0, 0, -12675, 63250]\)	\(19307236/11025\)	\(128595600000000\)	\([2, 2]\)	\(49152\)	\(1.3971\)
25200.el4	25200bm3	\([0, 0, 0, 50325, 504250]\)	\(604223422/354375\)	\(-8266860000000000\)	\([2]\)	\(98304\)	\(1.7437\)
25200.el1	25200bm4	\([0, 0, 0, -147675, 21798250]\)	\(15267472418/36015\)	\(840157920000000\)	\([4]\)	\(98304\)	\(1.7437\)