Elliptic curve isogeny class with Cremona label 68400gl (LMFDB label 68400.bh)

• Label: 68400gl
• Number of curves: $2$
• Conductor: $68400$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 68400gl have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1\)
\(19\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 5 T + 7 T^{2}\)	1.7.af
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 - 3 T + 29 T^{2}\)	1.29.ad
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 68400gl do not have complex multiplication.

Modular form 68400.2.a.gl

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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 68400gl

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
68400.bh1	68400gl1	\([0, 0, 0, -2862075, -1863982550]\)	\(-1389310279182025/267418692\)	\(-499067459758080000\)	\([]\)	\(1382400\)	\(2.3964\)	\(\Gamma_0(N)\)-optimal
68400.bh2	68400gl2	\([0, 0, 0, 17179125, 1631736250]\)	\(480705753733655/279172334592\)	\(-325626611068108800000000\)	\([]\)	\(6912000\)	\(3.2011\)