Elliptic curve isogeny class with Cremona label 130050bb (LMFDB label 130050.ef)

• Label: 130050bb
• Number of curves: $2$
• Conductor: $130050$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 130050bb have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1\)
\(5\)	\(1\)
\(17\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 130050bb do not have complex multiplication.

Modular form 130050.2.a.bb

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 130050bb

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
130050.ef2	130050bb1	\([1, -1, 1, -360905, 84001097]\)	\(-1579268174113/10077696\)	\(-33174672984000000\)	\([]\)	\(1959552\)	\(2.0073\)	\(\Gamma_0(N)\)-optimal
130050.ef1	130050bb2	\([1, -1, 1, -29277905, 60983203097]\)	\(-843137281012581793/216\)	\(-711048375000\)	\([]\)	\(5878656\)	\(2.5566\)