Elliptic curve isogeny class with LMFDB label 363888.t (Cremona label 363888t)

• Label: 363888.t
• Number of curves: $4$
• Conductor: $363888$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 363888.t have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(7\)	\(1 - T\)
\(19\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 363888.t do not have complex multiplication.

Modular form 363888.2.a.t

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 363888.t

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
363888.t1	363888t4	\([0, 0, 0, -326434611, -2270075559950]\)	\(27384399945278713/153257496\)	\(21529344520510785552384\)	\([2]\)	\(53084160\)	\(3.4775\)
363888.t2	363888t2	\([0, 0, 0, -20768691, -34129355150]\)	\(7052482298233/499254336\)	\(70134374393686104735744\)	\([2, 2]\)	\(26542080\)	\(3.1310\)
363888.t3	363888t1	\([0, 0, 0, -4133811, 2597132914]\)	\(55611739513/11440128\)	\(1607089137556717043712\)	\([2]\)	\(13271040\)	\(2.7844\)	\(\Gamma_0(N)\)-optimal
363888.t4	363888t3	\([0, 0, 0, 18739149, -148678386446]\)	\(5180411077127/70976229912\)	\(-9970616422849756823912448\)	\([2]\)	\(53084160\)	\(3.4775\)