Elliptic curve isogeny class with Cremona label 346560ij (LMFDB label 346560.ij)

• Label: 346560ij
• Number of curves: $2$
• Conductor: $346560$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 346560ij have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1 + T\)
\(19\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 346560ij do not have complex multiplication.

Modular form 346560.2.a.ij

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 Cremona numbering.

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

Isogeny graph

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

Elliptic curves in class 346560ij

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
346560.ij2	346560ij1	\([0, 1, 0, 512139, 137364939]\)	\(44957696/50625\)	\(-16728130252863360000\)	\([2]\)	\(7004160\)	\(2.3751\)	\(\Gamma_0(N)\)-optimal
346560.ij1	346560ij2	\([0, 1, 0, -2917361, 1291734639]\)	\(519388144/164025\)	\(867186272308436582400\)	\([2]\)	\(14008320\)	\(2.7217\)