Elliptic curve isogeny class with Cremona label 80850cc (LMFDB label 80850.bz)

• Label: 80850cc
• Number of curves: $4$
• Conductor: $80850$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 80850cc have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1 - T\)
\(5\)	\(1\)
\(7\)	\(1\)
\(11\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 - 7 T + 17 T^{2}\)	1.17.ah
\(19\)	\( 1 + T + 19 T^{2}\)	1.19.b
\(23\)	\( 1 + T + 23 T^{2}\)	1.23.b
\(29\)	\( 1 - 3 T + 29 T^{2}\)	1.29.ad
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 80850cc do not have complex multiplication.

Modular form 80850.2.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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 80850cc

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
80850.bz3	80850cc1	\([1, 0, 1, -393251, 72522398]\)	\(3658671062929/880165440\)	\(1617977872665000000\)	\([2]\)	\(1990656\)	\(2.2051\)	\(\Gamma_0(N)\)-optimal
80850.bz4	80850cc2	\([1, 0, 1, 929749, 456192398]\)	\(48351870250991/76871856600\)	\(-141310891517709375000\)	\([2]\)	\(3981312\)	\(2.5517\)
80850.bz1	80850cc3	\([1, 0, 1, -29719751, 62358921398]\)	\(1579250141304807889/41926500\)	\(77072043726562500\)	\([2]\)	\(5971968\)	\(2.7544\)
80850.bz2	80850cc4	\([1, 0, 1, -29683001, 62520841898]\)	\(-1573398910560073969/8138108343750\)	\(-14960004820841308593750\)	\([2]\)	\(11943936\)	\(3.1010\)