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

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

Rank

The elliptic curves in class 327600i have rank \(2\).

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
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 2 T + 23 T^{2}\)	1.23.c
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 327600.2.a.i

Isogeny matrix

The \((i,j)\)-th 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, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 327600i

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
327600.i2	327600i1	\([0, 0, 0, 1005, -5150]\)	\(1203052/819\)	\(-76422528000\)	\([2]\)	\(335872\)	\(0.77695\)	\(\Gamma_0(N)\)-optimal
327600.i1	327600i2	\([0, 0, 0, -4395, -42950]\)	\(50307514/24843\)	\(4636300032000\)	\([2]\)	\(671744\)	\(1.1235\)