Elliptic curve isogeny class with Cremona label 70560bi (LMFDB label 70560.df)

• Label: 70560bi
• Number of curves: $4$
• Conductor: $70560$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 70560bi have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + T + 23 T^{2}\)	1.23.b
\(29\)	\( 1 - T + 29 T^{2}\)	1.29.ab
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 70560bi do not have complex multiplication.

Modular form 70560.2.a.bi

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 70560bi

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
70560.df3	70560bi1	\([0, 0, 0, -13377, 573496]\)	\(48228544/2025\)	\(11115289281600\)	\([2, 2]\)	\(147456\)	\(1.2680\)	\(\Gamma_0(N)\)-optimal
70560.df4	70560bi2	\([0, 0, 0, 6468, 2129344]\)	\(85184/5625\)	\(-1976051427840000\)	\([2]\)	\(294912\)	\(1.6146\)
70560.df2	70560bi3	\([0, 0, 0, -35427, -1803494]\)	\(111980168/32805\)	\(1440541490895360\)	\([2]\)	\(294912\)	\(1.6146\)
70560.df1	70560bi4	\([0, 0, 0, -211827, 37524886]\)	\(23937672968/45\)	\(1976051427840\)	\([2]\)	\(294912\)	\(1.6146\)