Elliptic curve isogeny class with LMFDB label 126126.dr (Cremona label 126126dz)

• Label: 126126.dr
• Number of curves: $2$
• Conductor: $126126$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 126126.dr have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1\)
\(7\)	\(1\)
\(11\)	\(1 + T\)
\(13\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(17\)	\( 1 + 8 T + 17 T^{2}\)	1.17.i
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 + 8 T + 29 T^{2}\)	1.29.i
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 126126.dr do not have complex multiplication.

Modular form 126126.2.a.dr

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 126126.dr

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
126126.dr1	126126dz2	\([1, -1, 1, -6611640986, -206922891839975]\)	\(13802951728468271053322091/158357056\)	\(366705101504693952\)	\([2]\)	\(76308480\)	\(3.8700\)
126126.dr2	126126dz1	\([1, -1, 1, -413227226, -3233098224359]\)	\(-3369853043629824680811/11414181695488\)	\(-26431652387102641975296\)	\([2]\)	\(38154240\)	\(3.5234\)	\(\Gamma_0(N)\)-optimal