Elliptic curve isogeny class with Cremona label 76230bt (LMFDB label 76230.bh)

• Label: 76230bt
• Number of curves: $4$
• Conductor: $76230$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 76230bt have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 4 T + 17 T^{2}\)	1.17.ae
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 76230bt do not have complex multiplication.

Modular form 76230.2.a.bt

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 76230bt

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
76230.bh3	76230bt1	\([1, -1, 0, -994824, 383781888]\)	\(-84309998289049/414124480\)	\(-534828501098781120\)	\([2]\)	\(1658880\)	\(2.2499\)	\(\Gamma_0(N)\)-optimal
76230.bh2	76230bt2	\([1, -1, 0, -15935904, 24489720360]\)	\(346553430870203929/8300600\)	\(10719959023481400\)	\([2]\)	\(3317760\)	\(2.5965\)
76230.bh4	76230bt3	\([1, -1, 0, 2473641, 2035678365]\)	\(1296134247276791/2137096192000\)	\(-2759991278639874048000\)	\([2]\)	\(4976640\)	\(2.7992\)
76230.bh1	76230bt4	\([1, -1, 0, -17041239, 20898761373]\)	\(423783056881319689/99207416000000\)	\(128123200051258104000000\)	\([2]\)	\(9953280\)	\(3.1458\)