Elliptic curve isogeny class with LMFDB label 143325.er (Cremona label 143325ei)

• Label: 143325.er
• Number of curves: $4$
• Conductor: $143325$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 143325.er have rank \(0\).

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
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 143325.2.a.er

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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 143325.er

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
143325.er1	143325ei3	\([1, -1, 0, -6212817, 5961249216]\)	\(19790357598649/2998905\)	\(4018819517148515625\)	\([2]\)	\(3538944\)	\(2.5825\)
143325.er2	143325ei4	\([1, -1, 0, -2574567, -1531230534]\)	\(1408317602329/58524375\)	\(78428259807802734375\)	\([2]\)	\(3538944\)	\(2.5825\)
143325.er3	143325ei2	\([1, -1, 0, -424692, 74726091]\)	\(6321363049/1863225\)	\(2496899700003515625\)	\([2, 2]\)	\(1769472\)	\(2.2359\)
143325.er4	143325ei1	\([1, -1, 0, 71433, 7749216]\)	\(30080231/36855\)	\(-49389224835234375\)	\([2]\)	\(884736\)	\(1.8893\)	\(\Gamma_0(N)\)-optimal