Elliptic curve isogeny class with Cremona label 93600bh (LMFDB label 93600.co)

• Label: 93600bh
• Number of curves: $4$
• Conductor: $93600$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 93600bh have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 + 2 T + 11 T^{2}\)	1.11.c
\(17\)	\( 1 + 4 T + 17 T^{2}\)	1.17.e
\(19\)	\( 1 - T + 19 T^{2}\)	1.19.ab
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 + 9 T + 29 T^{2}\)	1.29.j
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 93600bh do not have complex multiplication.

Modular form 93600.2.a.bh

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 93600bh

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
93600.co3	93600bh1	\([0, 0, 0, -14925, -654500]\)	\(504358336/38025\)	\(27720225000000\)	\([2, 2]\)	\(147456\)	\(1.3247\)	\(\Gamma_0(N)\)-optimal
93600.co4	93600bh2	\([0, 0, 0, 14325, -2906750]\)	\(55742968/658125\)	\(-3838185000000000\)	\([2]\)	\(294912\)	\(1.6712\)
93600.co2	93600bh3	\([0, 0, 0, -48675, 3361750]\)	\(2186875592/428415\)	\(2498516280000000\)	\([4]\)	\(294912\)	\(1.6712\)
93600.co1	93600bh4	\([0, 0, 0, -234300, -43652000]\)	\(30488290624/195\)	\(9097920000000\)	\([2]\)	\(294912\)	\(1.6712\)