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

• Label: 327600.gt
• Number of curves: $4$
• Conductor: $327600$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 327600.gt 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.g
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 327600.2.a.gt

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.

\(\left(\begin{array}{rrrr} 1 & 3 & 2 & 6 \\ 3 & 1 & 6 & 2 \\ 2 & 6 & 1 & 3 \\ 6 & 2 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 327600.gt

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
327600.gt1	327600gt4	\([0, 0, 0, -57570075, -154297149750]\)	\(16751080718799363/1529437000000\)	\(1926650142144000000000000\)	\([2]\)	\(47775744\)	\(3.3990\)
327600.gt2	327600gt2	\([0, 0, 0, -56244075, -162354107750]\)	\(11387025941627437947/10765300\)	\(18602438400000000\)	\([2]\)	\(15925248\)	\(2.8497\)
327600.gt3	327600gt3	\([0, 0, 0, -12642075, 14587202250]\)	\(177381177331203/29679104000\)	\(37387123458048000000000\)	\([2]\)	\(23887872\)	\(3.0524\)
327600.gt4	327600gt1	\([0, 0, 0, -3516075, -2535539750]\)	\(2781982314427707/2703013040\)	\(4670806533120000000\)	\([2]\)	\(7962624\)	\(2.5031\)	\(\Gamma_0(N)\)-optimal