Elliptic curve isogeny class with Cremona label 25168s (LMFDB label 25168.bf)

• Label: 25168s
• Number of curves: $2$
• Conductor: $25168$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 25168s have rank \(1\).

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 \(\mathbb{F}_p\)
\(3\)	\( 1 + T + 3 T^{2}\)	1.3.b
\(5\)	\( 1 - 3 T + 5 T^{2}\)	1.5.ad
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 - 3 T + 23 T^{2}\)	1.23.ad
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 25168.2.a.s

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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 25168s

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
25168.bf2	25168s1	\([0, 1, 0, 542040, 23735732]\)	\(2427173723519/1437646496\)	\(-10432014188954648576\)	\([]\)	\(345600\)	\(2.3386\)	\(\Gamma_0(N)\)-optimal
25168.bf1	25168s2	\([0, 1, 0, -54072520, -153097872908]\)	\(-2409558590804994721/674373039626\)	\(-4893462431550980857856\)	\([]\)	\(1728000\)	\(3.1433\)