Elliptic curve isogeny class with LMFDB label 340704.ct (Cremona label 340704ct)

• Label: 340704.ct
• Number of curves: $2$
• Conductor: $340704$
• CM: no
• Rank: $2$

Rank

The elliptic curves in class 340704.ct have rank \(2\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(7\)	\(1 - T\)
\(13\)	\(1\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 340704.ct do not have complex multiplication.

Modular form 340704.2.a.ct

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 340704.ct

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
340704.ct1	340704ct2	\([0, 0, 0, -4875, 94302]\)	\(421875000/117649\)	\(3573156367872\)	\([2]\)	\(387072\)	\(1.1159\)
340704.ct2	340704ct1	\([0, 0, 0, -4485, 115596]\)	\(2628072000/343\)	\(1302170688\)	\([2]\)	\(193536\)	\(0.76934\)	\(\Gamma_0(N)\)-optimal