Elliptic curve isogeny class with Cremona label 124800cr (LMFDB label 124800.eb)

• Label: 124800cr
• Number of curves: $2$
• Conductor: $124800$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 124800cr have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 - 2 T + 23 T^{2}\)	1.23.ac
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 124800cr do not have complex multiplication.

Modular form 124800.2.a.cr

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 124800cr

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
124800.eb1	124800cr1	\([0, 1, 0, -721958, 235793838]\)	\(166463915033056/62462907\)	\(15615726750000000\)	\([2]\)	\(1863680\)	\(2.0741\)	\(\Gamma_0(N)\)-optimal
124800.eb2	124800cr2	\([0, 1, 0, -616333, 307301963]\)	\(-809134470272/808321761\)	\(-25866296352000000000\)	\([2]\)	\(3727360\)	\(2.4207\)