Elliptic curve isogeny class with LMFDB label 252150.cm (Cremona label 252150cm)

• Label: 252150.cm
• Number of curves: $2$
• Conductor: $252150$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 252150.cm have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1 - T\)
\(5\)	\(1\)
\(41\)	\(1\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 252150.cm do not have complex multiplication.

Modular form 252150.2.a.cm

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 252150.cm

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
252150.cm1	252150cm1	\([1, 0, 0, -19075001288, -1014017955791808]\)	\(10341755683137709164937/356992303104\)	\(26496103952791685376000000\)	\([2]\)	\(361267200\)	\(4.3759\)	\(\Gamma_0(N)\)-optimal
252150.cm2	252150cm2	\([1, 0, 0, -19048105288, -1017020060415808]\)	\(-10298071306410575356297/60769798505543808\)	\(-4510357462592173506126402000000\)	\([2]\)	\(722534400\)	\(4.7225\)