Elliptic curve isogeny class with Cremona label 38025cp (LMFDB label 38025.dc)

• Label: 38025cp
• Number of curves: $2$
• Conductor: $38025$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 38025cp have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1\)
\(5\)	\(1\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 - T + 2 T^{2}\)	1.2.ab
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 - T + 11 T^{2}\)	1.11.ab
\(17\)	\( 1 - 4 T + 17 T^{2}\)	1.17.ae
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 9 T + 23 T^{2}\)	1.23.j
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 38025cp do not have complex multiplication.

Modular form 38025.2.a.cp

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 38025cp

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
38025.dc1	38025cp1	\([0, 0, 1, -12675, 562981]\)	\(-102400/3\)	\(-6597644551875\)	\([]\)	\(112320\)	\(1.2387\)	\(\Gamma_0(N)\)-optimal
38025.dc2	38025cp2	\([0, 0, 1, 63375, -27119219]\)	\(20480/243\)	\(-334005755438671875\)	\([]\)	\(561600\)	\(2.0434\)