Elliptic curve isogeny class with Cremona label 327600go (LMFDB label 327600.go)

• Label: 327600go
• Number of curves: $2$
• Conductor: $327600$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 327600go have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1\)
\(7\)	\(1 + T\)
\(13\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 - 6 T + 11 T^{2}\)	1.11.ag
\(17\)	\( 1 + 2 T + 17 T^{2}\)	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.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 327600go do not have complex multiplication.

Modular form 327600.2.a.go

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 327600go

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
327600.go2	327600go1	\([0, 0, 0, -34635, -2462150]\)	\(12310389629/107653\)	\(40181266944000\)	\([2]\)	\(1032192\)	\(1.4342\)	\(\Gamma_0(N)\)-optimal
327600.go1	327600go2	\([0, 0, 0, -59835, 1595050]\)	\(63473450669/33787663\)	\(12611177639424000\)	\([2]\)	\(2064384\)	\(1.7808\)