Elliptic curve isogeny class with Cremona label 55770cx (LMFDB label 55770.da)

• Label: 55770cx
• Number of curves: $4$
• Conductor: $55770$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 55770cx have rank \(0\).

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 \(\mathbb{F}_p\)
\(7\)	\( 1 + 3 T + 7 T^{2}\)	1.7.d
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 - 3 T + 23 T^{2}\)	1.23.ad
\(29\)	\( 1 - T + 29 T^{2}\)	1.29.ab
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 55770.2.a.cx

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 55770cx

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
55770.da4	55770cx1	\([1, 0, 0, -5665, 2053817]\)	\(-4165509529/375289200\)	\(-1811449288162800\)	\([4]\)	\(258048\)	\(1.6073\)	\(\Gamma_0(N)\)-optimal
55770.da3	55770cx2	\([1, 0, 0, -279445, 56426525]\)	\(499980107400409/4140922500\)	\(19987441991302500\)	\([2, 2]\)	\(516096\)	\(1.9539\)
55770.da2	55770cx3	\([1, 0, 0, -477175, -33856993]\)	\(2489411558640889/1338278906250\)	\(6459616669197656250\)	\([2]\)	\(1032192\)	\(2.3005\)
55770.da1	55770cx4	\([1, 0, 0, -4462195, 3627658475]\)	\(2035678735521204409/141376950\)	\(682399534652550\)	\([2]\)	\(1032192\)	\(2.3005\)