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

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

Rank

The elliptic curves in class 346560ix 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 \(\mathbb{F}_p\)
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 + 6 T + 11 T^{2}\)	1.11.g
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 8 T + 29 T^{2}\)	1.29.i
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 346560.2.a.ix

Isogeny matrix

The \(i,j\) 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.

Elliptic curves in class 346560ix

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
346560.ix2	346560ix1	\([0, 1, 0, -2276225, 1449540735]\)	\(-105756712489/12476160\)	\(-153865929017775882240\)	\([2]\)	\(13271040\)	\(2.6094\)	\(\Gamma_0(N)\)-optimal
346560.ix1	346560ix2	\([0, 1, 0, -37394305, 88001560703]\)	\(468898230633769/5540400\)	\(68328619794078105600\)	\([2]\)	\(26542080\)	\(2.9559\)