Elliptic curve isogeny class with Cremona label 143325eq (LMFDB label 143325.ez)

• Label: 143325eq
• Number of curves: $2$
• Conductor: $143325$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 143325eq have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1\)
\(5\)	\(1\)
\(7\)	\(1\)
\(13\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 - T + 2 T^{2}\)	1.2.ab
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 5 T + 19 T^{2}\)	1.19.f
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 - 3 T + 29 T^{2}\)	1.29.ad
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 143325eq do not have complex multiplication.

Modular form 143325.2.a.eq

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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 143325eq

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
143325.ez1	143325eq1	\([1, -1, 0, -1181742, 494854541]\)	\(-56723625/13\)	\(-41828405230828125\)	\([]\)	\(1935360\)	\(2.1809\)	\(\Gamma_0(N)\)-optimal
143325.ez2	143325eq2	\([1, -1, 0, 6921633, -20452369834]\)	\(11397810375/62748517\)	\(-201897722823808271203125\)	\([]\)	\(13547520\)	\(3.1539\)