Elliptic curve isogeny class with LMFDB label 24300.m (Cremona label 24300p)

• Label: 24300.m
• Number of curves: $2$
• Conductor: $24300$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 24300.m have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 24300.m do not have complex multiplication.

Modular form 24300.2.a.m

Isogeny matrix

The \((i,j)\)-th 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, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 24300.m

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
24300.m1	24300p2	\([0, 0, 0, -14175, 465750]\)	\(444528/125\)	\(88573500000000\)	\([]\)	\(46656\)	\(1.3832\)
24300.m2	24300p1	\([0, 0, 0, -5175, -143250]\)	\(15768432/5\)	\(4860000000\)	\([]\)	\(15552\)	\(0.83392\)	\(\Gamma_0(N)\)-optimal