Elliptic curve isogeny class with Cremona label 365296bl (LMFDB label 365296.bl)

• Label: 365296bl
• Number of curves: $2$
• Conductor: $365296$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 365296bl have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(17\)	\(1\)
\(79\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - 2 T + 3 T^{2}\)	1.3.ac
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(11\)	\( 1 + 2 T + 11 T^{2}\)	1.11.c
\(13\)	\( 1 + 6 T + 13 T^{2}\)	1.13.g
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 - 4 T + 29 T^{2}\)	1.29.ae
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 365296bl do not have complex multiplication.

Modular form 365296.2.a.bl

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 365296bl

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
365296.bl2	365296bl1	\([0, -1, 0, -13377328, 15904466880]\)	\(2677801592364625/445003071488\)	\(43996333437966469824512\)	\([2]\)	\(36495360\)	\(3.0662\)	\(\Gamma_0(N)\)-optimal
365296.bl1	365296bl2	\([0, -1, 0, -60727088, -167017125952]\)	\(250505699702316625/23053462341632\)	\(2279237787484340111802368\)	\([2]\)	\(72990720\)	\(3.4127\)