Elliptic curve isogeny class with LMFDB label 1764.i (Cremona label 1764g)

• Label: 1764.i
• Number of curves: $2$
• Conductor: $1764$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 1764.i have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(7\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(11\)	\( 1 + 2 T + 11 T^{2}\)	1.11.c
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 8 T + 19 T^{2}\)	1.19.i
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 - 10 T + 29 T^{2}\)	1.29.ak
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 1764.i do not have complex multiplication.

Modular form 1764.2.a.i

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 1764.i

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
1764.i1	1764g2	\([0, 0, 0, -399, -2842]\)	\(109744/9\)	\(576108288\)	\([2]\)	\(768\)	\(0.42353\)
1764.i2	1764g1	\([0, 0, 0, -84, 245]\)	\(16384/3\)	\(12002256\)	\([2]\)	\(384\)	\(0.076952\)	\(\Gamma_0(N)\)-optimal