Elliptic curve isogeny class with LMFDB label 1764.a (Cremona label 1764e)

• Label: 1764.a
• Number of curves: $2$
• Conductor: $1764$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 1764.a have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

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

See L-function page for more information

Complex multiplication

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

Modular form 1764.2.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.

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

Isogeny graph

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

Elliptic curves in class 1764.a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
1764.a1	1764e2	\([0, 0, 0, -62769, 6052921]\)	\(406749952\)	\(67240638864\)	\([3]\)	\(3780\)	\(1.3172\)
1764.a2	1764e1	\([0, 0, 0, -1029, 2401]\)	\(1792\)	\(67240638864\)	\([]\)	\(1260\)	\(0.76792\)	\(\Gamma_0(N)\)-optimal