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

• Label: 346560f
• Number of curves: $4$
• Conductor: $346560$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 346560f 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.e
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 346560.2.a.f

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 346560f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
346560.f3	346560f1	\([0, -1, 0, -137661, -19612515]\)	\(5988775936/285\)	\(13729869911040\)	\([2]\)	\(1474560\)	\(1.5945\)	\(\Gamma_0(N)\)-optimal
346560.f2	346560f2	\([0, -1, 0, -144881, -17433519]\)	\(436334416/81225\)	\(62608206794342400\)	\([2, 2]\)	\(2949120\)	\(1.9411\)
346560.f1	346560f3	\([0, -1, 0, -693601, 206553985]\)	\(11968836484/961875\)	\(2965651900784640000\)	\([2]\)	\(5898240\)	\(2.2877\)
346560.f4	346560f4	\([0, -1, 0, 288319, -102080799]\)	\(859687196/1954815\)	\(-6027083374068695040\)	\([2]\)	\(5898240\)	\(2.2877\)