Elliptic curve isogeny class with Cremona label 365040t (LMFDB label 365040.t)

• Label: 365040t
• Number of curves: $2$
• Conductor: $365040$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 365040t have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 + 3 T + 11 T^{2}\)	1.11.d
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 - 9 T + 23 T^{2}\)	1.23.aj
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 365040t do not have complex multiplication.

Modular form 365040.2.a.t

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 365040t

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
365040.t2	365040t1	\([0, 0, 0, -744783, -247395382]\)	\(8103309552/25\)	\(140958268588800\)	\([]\)	\(3234816\)	\(1.9414\)	\(\Gamma_0(N)\)-optimal
365040.t1	365040t2	\([0, 0, 0, -1008423, -57064878]\)	\(27591408/15625\)	\(64224111125772000000\)	\([]\)	\(9704448\)	\(2.4907\)