Elliptic curve isogeny class with Cremona label 25200cu (LMFDB label 25200.eo)

• Label: 25200cu
• Number of curves: $2$
• Conductor: $25200$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 25200cu 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 \(\mathbb{F}_p\)
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 25200.2.a.cu

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 25200cu

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
25200.eo2	25200cu1	\([0, 0, 0, 165, 1930]\)	\(179685/686\)	\(-1896652800\)	\([]\)	\(6912\)	\(0.46307\)	\(\Gamma_0(N)\)-optimal
25200.eo1	25200cu2	\([0, 0, 0, -8235, 288090]\)	\(-30642435/56\)	\(-112870195200\)	\([]\)	\(20736\)	\(1.0124\)