Elliptic curve isogeny class with Cremona label 25168bp (LMFDB label 25168.bm)

• Label: 25168bp
• Number of curves: $2$
• Conductor: $25168$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 25168bp have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(11\)	\(1\)
\(13\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - 3 T + 3 T^{2}\)	1.3.ad
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(17\)	\( 1 + 7 T + 17 T^{2}\)	1.17.h
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 - 7 T + 23 T^{2}\)	1.23.ah
\(29\)	\( 1 + 9 T + 29 T^{2}\)	1.29.j
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 25168bp do not have complex multiplication.

Modular form 25168.2.a.bp

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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 25168bp

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
25168.bm2	25168bp1	\([0, 0, 0, -5203, 220946]\)	\(-2146689/1664\)	\(-12074506256384\)	\([]\)	\(67200\)	\(1.2089\)	\(\Gamma_0(N)\)-optimal
25168.bm1	25168bp2	\([0, 0, 0, -411763, -111583054]\)	\(-1064019559329/125497034\)	\(-910645866701103104\)	\([]\)	\(470400\)	\(2.1819\)