Elliptic curve isogeny class with Cremona label 24300o (LMFDB label 24300.r)

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

Rank

The elliptic curves in class 24300o 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
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + 5 T + 13 T^{2}\)	1.13.f
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 - 8 T + 19 T^{2}\)	1.19.ai
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 24300.2.a.o

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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 24300o

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
24300.r2	24300o1	\([0, 0, 0, -1575, -17250]\)	\(444528/125\)	\(121500000000\)	\([]\)	\(15552\)	\(0.83392\)	\(\Gamma_0(N)\)-optimal
24300.r1	24300o2	\([0, 0, 0, -46575, 3867750]\)	\(15768432/5\)	\(3542940000000\)	\([]\)	\(46656\)	\(1.3832\)