Elliptic curve isogeny class with LMFDB label 65520.cc (Cremona label 65520do)

• Label: 65520.cc
• Number of curves: $4$
• Conductor: $65520$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 65520.cc have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1 - T\)
\(7\)	\(1 + T\)
\(13\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 10 T + 29 T^{2}\)	1.29.ak
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 65520.cc do not have complex multiplication.

Modular form 65520.2.a.cc

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 65520.cc

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
65520.cc1	65520do4	\([0, 0, 0, -3479187, 2495790866]\)	\(1559802282754777489/1481059636875\)	\(4422420378754560000\)	\([2]\)	\(1769472\)	\(2.4996\)
65520.cc2	65520do2	\([0, 0, 0, -268707, 19226594]\)	\(718576775407009/362361861225\)	\(1082006719828070400\)	\([2, 2]\)	\(884736\)	\(2.1531\)
65520.cc3	65520do1	\([0, 0, 0, -147027, -21487534]\)	\(117713838907729/1322517105\)	\(3949014915256320\)	\([2]\)	\(442368\)	\(1.8065\)	\(\Gamma_0(N)\)-optimal
65520.cc4	65520do3	\([0, 0, 0, 994893, 148366514]\)	\(36472485598112591/24291459037755\)	\(-72533908023391825920\)	\([2]\)	\(1769472\)	\(2.4996\)