Elliptic curve isogeny class with LMFDB label 289800.ds (Cremona label 289800ds)

• Label: 289800.ds
• Number of curves: $2$
• Conductor: $289800$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 289800.ds have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1\)
\(7\)	\(1 - T\)
\(23\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 289800.ds do not have complex multiplication.

Modular form 289800.2.a.ds

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 LMFDB numbering.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 289800.ds

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
289800.ds1	289800ds1	\([0, 0, 0, -9075, -45250]\)	\(7086244/4025\)	\(46947600000000\)	\([2]\)	\(589824\)	\(1.3132\)	\(\Gamma_0(N)\)-optimal
289800.ds2	289800ds2	\([0, 0, 0, 35925, -360250]\)	\(219804478/129605\)	\(-3023425440000000\)	\([2]\)	\(1179648\)	\(1.6598\)