Elliptic curve isogeny class with Cremona label 122694cm (LMFDB label 122694.cp)

• Label: 122694cm
• Number of curves: $4$
• Conductor: $122694$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 122694cm have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - T + 5 T^{2}\)	1.5.ab
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(17\)	\( 1 - T + 17 T^{2}\)	1.17.ab
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 3 T + 29 T^{2}\)	1.29.d
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 122694cm do not have complex multiplication.

Modular form 122694.2.a.cm

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 122694cm

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
122694.cp4	122694cm1	\([1, 1, 1, -3149572, -2502541579]\)	\(-404075127457/82223856\)	\(-703095089117212821744\)	\([2]\)	\(5806080\)	\(2.7225\)	\(\Gamma_0(N)\)-optimal
122694.cp3	122694cm2	\([1, 1, 1, -52636152, -147003355179]\)	\(1886079023633377/59629284\)	\(509889207190375414116\)	\([2, 2]\)	\(11612160\)	\(3.0691\)
122694.cp2	122694cm3	\([1, 1, 1, -54885542, -133757147347]\)	\(2138362647385537/333926700822\)	\(2855402737048247336113878\)	\([2]\)	\(23224320\)	\(3.4157\)
122694.cp1	122694cm4	\([1, 1, 1, -842172042, -9407311901811]\)	\(7725203825376001537/7722\)	\(66030718361871978\)	\([2]\)	\(23224320\)	\(3.4157\)