Elliptic curve isogeny class with Cremona label 36300ci (LMFDB label 36300.ce)

• Label: 36300ci
• Number of curves: $2$
• Conductor: $36300$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 36300ci have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1\)
\(11\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 3 T + 7 T^{2}\)	1.7.ad
\(13\)	\( 1 - 5 T + 13 T^{2}\)	1.13.af
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 - 4 T + 29 T^{2}\)	1.29.ae
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 36300ci do not have complex multiplication.

Modular form 36300.2.a.ci

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 36300ci

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
36300.ce2	36300ci1	\([0, 1, 0, -18553, -936652]\)	\(199344128/9801\)	\(34726138722000\)	\([2]\)	\(92160\)	\(1.3575\)	\(\Gamma_0(N)\)-optimal
36300.ce1	36300ci2	\([0, 1, 0, -51828, 3322548]\)	\(271593488/72171\)	\(4091370525792000\)	\([2]\)	\(184320\)	\(1.7041\)