Elliptic curve isogeny class with LMFDB label 6845.a (Cremona label 6845c)

• Label: 6845.a
• Number of curves: $2$
• Conductor: $6845$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 6845.a have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(5\)	\(1 - T\)
\(37\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + T + 2 T^{2}\)	1.2.b
\(3\)	\( 1 + 2 T + 3 T^{2}\)	1.3.c
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 6845.a do not have complex multiplication.

Modular form 6845.2.a.a

Isogeny matrix

The \((i,j)\)-th 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.

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

Isogeny graph

The vertices are labelled with LMFDB labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 6845.a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
6845.a1	6845c1	\([1, 0, 0, -4820, -124865]\)	\(4826809/185\)	\(474659385665\)	\([2]\)	\(8208\)	\(1.0084\)	\(\Gamma_0(N)\)-optimal
6845.a2	6845c2	\([1, 0, 0, 2025, -449318]\)	\(357911/34225\)	\(-87811986348025\)	\([2]\)	\(16416\)	\(1.3550\)