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

• Label: 248430f
• Number of curves: $2$
• Conductor: $248430$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 248430f 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 \(\mathbb{F}_p\)
\(11\)	\( 1 + 3 T + 11 T^{2}\)	1.11.d
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 + 3 T + 23 T^{2}\)	1.23.d
\(29\)	\( 1 - 9 T + 29 T^{2}\)	1.29.aj
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 248430.2.a.f

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 248430f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
248430.f2	248430f1	\([1, 1, 0, 778242, -473044788]\)	\(543164999/1323000\)	\(-126968182456091067000\)	\([]\)	\(9704448\)	\(2.5414\)	\(\Gamma_0(N)\)-optimal
248430.f1	248430f2	\([1, 1, 0, -7295733, 16067300397]\)	\(-447502578601/903544320\)	\(-86713061284145678753280\)	\([]\)	\(29113344\)	\(3.0907\)