Elliptic curve isogeny class with Cremona label 92400cb (LMFDB label 92400.ft)

• Label: 92400cb
• Number of curves: $4$
• Conductor: $92400$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 92400cb have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(5\)	\(1\)
\(7\)	\(1 - T\)
\(11\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(19\)	\( 1 - 3 T + 19 T^{2}\)	1.19.ad
\(23\)	\( 1 + T + 23 T^{2}\)	1.23.b
\(29\)	\( 1 + 7 T + 29 T^{2}\)	1.29.h
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 92400cb do not have complex multiplication.

Modular form 92400.2.a.cb

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 92400cb

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
92400.ft3	92400cb1	\([0, 1, 0, -28908, 1882188]\)	\(667932971344/3465\)	\(13860000000\)	\([2]\)	\(147456\)	\(1.1426\)	\(\Gamma_0(N)\)-optimal
92400.ft2	92400cb2	\([0, 1, 0, -29408, 1813188]\)	\(175798419556/12006225\)	\(192099600000000\)	\([2, 2]\)	\(294912\)	\(1.4892\)
92400.ft4	92400cb3	\([0, 1, 0, 25592, 7863188]\)	\(57925453822/866412855\)	\(-27725211360000000\)	\([2]\)	\(589824\)	\(1.8357\)
92400.ft1	92400cb4	\([0, 1, 0, -92408, -8644812]\)	\(2727138195938/576489375\)	\(18447660000000000\)	\([2]\)	\(589824\)	\(1.8357\)