Elliptic curve isogeny class with LMFDB label 248430.in (Cremona label 248430in)

• Label: 248430.in
• Number of curves: $4$
• Conductor: $248430$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 248430.in have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1 - T\)
\(5\)	\(1 + T\)
\(7\)	\(1\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 10 T + 29 T^{2}\)	1.29.k
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 248430.in do not have complex multiplication.

Modular form 248430.2.a.in

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 248430.in

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
248430.in1	248430in3	\([1, 0, 0, -4004036, 3082981446]\)	\(12501706118329/2570490\)	\(1459702233678870090\)	\([2]\)	\(8257536\)	\(2.4825\)
248430.in2	248430in2	\([1, 0, 0, -277586, 36981216]\)	\(4165509529/1368900\)	\(777356219118924900\)	\([2, 2]\)	\(4128768\)	\(2.1359\)
248430.in3	248430in1	\([1, 0, 0, -111966, -13996620]\)	\(273359449/9360\)	\(5315256199103760\)	\([2]\)	\(2064384\)	\(1.7893\)	\(\Gamma_0(N)\)-optimal
248430.in4	248430in4	\([1, 0, 0, 798944, 254224970]\)	\(99317171591/106616250\)	\(-60544090142916266250\)	\([2]\)	\(8257536\)	\(2.4825\)