Elliptic curve isogeny class with Cremona label 126126cb (LMFDB label 126126.d)

• Label: 126126cb
• Number of curves: $2$
• Conductor: $126126$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 126126cb have rank \(1\).

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 \(\mathbb{F}_p\)
\(5\)	\( 1 - T + 5 T^{2}\)	1.5.ab
\(17\)	\( 1 + 5 T + 17 T^{2}\)	1.17.f
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 - 3 T + 23 T^{2}\)	1.23.ad
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 126126.2.a.cb

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 126126cb

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
126126.d1	126126cb1	\([1, -1, 0, -11431611, 127491600613]\)	\(-802302449299393/33632965656576\)	\(-6925850174019870729732096\)	\([]\)	\(29030400\)	\(3.4465\)	\(\Gamma_0(N)\)-optimal
126126.d2	126126cb2	\([1, -1, 0, 102663909, -3401094908219]\)	\(581124479497931327/24602777889339936\)	\(-5066313665769201800220922656\)	\([]\)	\(87091200\)	\(3.9958\)