Elliptic curve isogeny class with Cremona label 15680cp (LMFDB label 15680.de)

• Label: 15680cp
• Number of curves: $4$
• Conductor: $15680$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 15680cp have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - T + 3 T^{2}\)	1.3.ab
\(11\)	\( 1 + 6 T + 11 T^{2}\)	1.11.g
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 - 3 T + 23 T^{2}\)	1.23.ad
\(29\)	\( 1 - 3 T + 29 T^{2}\)	1.29.ad
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 15680cp do not have complex multiplication.

Modular form 15680.2.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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 15680cp

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
15680.de3	15680cp1	\([0, -1, 0, -261, 1205]\)	\(16384/5\)	\(602362880\)	\([2]\)	\(5760\)	\(0.38958\)	\(\Gamma_0(N)\)-optimal
15680.de4	15680cp2	\([0, -1, 0, 719, 7281]\)	\(21296/25\)	\(-48189030400\)	\([2]\)	\(11520\)	\(0.73615\)
15680.de1	15680cp3	\([0, -1, 0, -8101, -277899]\)	\(488095744/125\)	\(15059072000\)	\([2]\)	\(17280\)	\(0.93888\)
15680.de2	15680cp4	\([0, -1, 0, -7121, -348655]\)	\(-20720464/15625\)	\(-30118144000000\)	\([2]\)	\(34560\)	\(1.2855\)