Elliptic curve isogeny class with LMFDB label 8001.c (Cremona label 8001g)

• Label: 8001.c
• Number of curves: $2$
• Conductor: $8001$
• CM: no
• Rank: $2$

Rank

The elliptic curves in class 8001.c have rank \(2\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1\)
\(7\)	\(1 - T\)
\(127\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + 2 T^{2}\)	1.2.a
\(5\)	\( 1 + 3 T + 5 T^{2}\)	1.5.d
\(11\)	\( 1 + 6 T + 11 T^{2}\)	1.11.g
\(13\)	\( 1 + T + 13 T^{2}\)	1.13.b
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 3 T + 23 T^{2}\)	1.23.d
\(29\)	\( 1 + 3 T + 29 T^{2}\)	1.29.d
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 8001.c do not have complex multiplication.

Modular form 8001.2.a.c

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

Elliptic curves in class 8001.c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
8001.c1	8001g2	\([0, 0, 1, -107544, 13574592]\)	\(188692544389906432/301112301\)	\(219510867429\)	\([3]\)	\(24192\)	\(1.4411\)
8001.c2	8001g1	\([0, 0, 1, -1704, 7227]\)	\(750593769472/403418421\)	\(294092028909\)	\([]\)	\(8064\)	\(0.89175\)	\(\Gamma_0(N)\)-optimal