Elliptic curve isogeny class with Cremona label 152100dk (LMFDB label 152100.bt)

• Label: 152100dk
• Number of curves: $2$
• Conductor: $152100$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 152100dk have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(17\)	\( 1 - 4 T + 17 T^{2}\)	1.17.ae
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 152100dk do not have complex multiplication.

Modular form 152100.2.a.dk

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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 152100dk

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
152100.bt2	152100dk1	\([0, 0, 0, 456300, 467137125]\)	\(442368/4225\)	\(-100350173634018750000\)	\([2]\)	\(4644864\)	\(2.5191\)	\(\Gamma_0(N)\)-optimal
152100.bt1	152100dk2	\([0, 0, 0, -6958575, 6539919750]\)	\(98055792/8125\)	\(3087697650277500000000\)	\([2]\)	\(9289728\)	\(2.8657\)