Elliptic curve isogeny class with LMFDB label 28350.bl (Cremona label 28350bo)

• Label: 28350.bl
• Number of curves: $2$
• Conductor: $28350$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 28350.bl have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 3 T + 11 T^{2}\)	1.11.d
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 28350.bl do not have complex multiplication.

Modular form 28350.2.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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 28350.bl

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
28350.bl1	28350bo2	\([1, -1, 1, -439805, -113487803]\)	\(-1812792825/25088\)	\(-130203045000000000\)	\([]\)	\(349920\)	\(2.0903\)
28350.bl2	28350bo1	\([1, -1, 1, 19570, -787803]\)	\(1047929175/941192\)	\(-744497578125000\)	\([]\)	\(116640\)	\(1.5410\)	\(\Gamma_0(N)\)-optimal