Elliptic curve isogeny class with LMFDB label 13950.da (Cremona label 13950by)

• Label: 13950.da
• Number of curves: $2$
• Conductor: $13950$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 13950.da have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1\)
\(5\)	\(1\)
\(31\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(13\)	\( 1 + 5 T + 13 T^{2}\)	1.13.f
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(19\)	\( 1 + 7 T + 19 T^{2}\)	1.19.h
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 13950.da do not have complex multiplication.

Modular form 13950.2.a.da

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 13950.da

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
13950.da1	13950by1	\([1, -1, 1, -1205, 34797]\)	\(-458314011/953312\)	\(-402178500000\)	\([]\)	\(25920\)	\(0.91580\)	\(\Gamma_0(N)\)-optimal
13950.da2	13950by2	\([1, -1, 1, 10420, -747953]\)	\(406869021/1015808\)	\(-312408576000000\)	\([]\)	\(77760\)	\(1.4651\)