Elliptic curve isogeny class with Cremona label 55770cm (LMFDB label 55770.cr)

• Label: 55770cm
• Number of curves: $2$
• Conductor: $55770$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 55770cm have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1 - T\)
\(5\)	\(1 + T\)
\(11\)	\(1 + T\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 5 T + 7 T^{2}\)	1.7.f
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 - 3 T + 23 T^{2}\)	1.23.ad
\(29\)	\( 1 + 3 T + 29 T^{2}\)	1.29.d
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 55770cm do not have complex multiplication.

Modular form 55770.2.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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 55770cm

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
55770.cr2	55770cm1	\([1, 0, 0, -112811, 19574385]\)	\(-32894113444921/15289560000\)	\(-73799785814040000\)	\([2]\)	\(645120\)	\(1.9429\)	\(\Gamma_0(N)\)-optimal
55770.cr1	55770cm2	\([1, 0, 0, -1971811, 1065447785]\)	\(175654575624148921/21954418200\)	\(105969783357523800\)	\([2]\)	\(1290240\)	\(2.2895\)