Elliptic curve isogeny class with LMFDB label 347600.bj (Cremona label 347600bj)

• Label: 347600.bj
• Number of curves: $4$
• Conductor: $347600$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 347600.bj have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1\)
\(11\)	\(1 - T\)
\(79\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 347600.bj do not have complex multiplication.

Modular form 347600.2.a.bj

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 LMFDB numbering.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 347600.bj

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
347600.bj1	347600bj3	\([0, 0, 0, -3278675, 2283139250]\)	\(121806044811730242/117823995025\)	\(3770367840800000000\)	\([2]\)	\(6684672\)	\(2.4855\)
347600.bj2	347600bj4	\([0, 0, 0, -2228675, -1268310750]\)	\(38257268424094242/423358789975\)	\(13547481279200000000\)	\([2]\)	\(6684672\)	\(2.4855\)
347600.bj3	347600bj2	\([0, 0, 0, -253675, 17414250]\)	\(112833156224484/57109050625\)	\(913744810000000000\)	\([2, 2]\)	\(3342336\)	\(2.1389\)
347600.bj4	347600bj1	\([0, 0, 0, 58825, 2101750]\)	\(5627940902064/3733984375\)	\(-14935937500000000\)	\([2]\)	\(1671168\)	\(1.7923\)	\(\Gamma_0(N)\)-optimal