Elliptic curve isogeny class with Cremona label 6150i (LMFDB label 6150.a)

• Label: 6150i
• Number of curves: $4$
• Conductor: $6150$
• CM: no
• Rank: $2$

Rank

The elliptic curves in class 6150i have rank \(2\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(13\)	\( 1 - T + 13 T^{2}\)	1.13.ab
\(17\)	\( 1 - 7 T + 17 T^{2}\)	1.17.ah
\(19\)	\( 1 - 5 T + 19 T^{2}\)	1.19.af
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 6150i do not have complex multiplication.

Modular form 6150.2.a.i

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 6150i

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
6150.a3	6150i1	\([1, 1, 0, -225, 1125]\)	\(81182737/5904\)	\(92250000\)	\([2]\)	\(3072\)	\(0.27471\)	\(\Gamma_0(N)\)-optimal
6150.a2	6150i2	\([1, 1, 0, -725, -6375]\)	\(2703045457/544644\)	\(8510062500\)	\([2, 2]\)	\(6144\)	\(0.62129\)
6150.a1	6150i3	\([1, 1, 0, -10975, -447125]\)	\(9357915116017/538002\)	\(8406281250\)	\([2]\)	\(12288\)	\(0.96786\)
6150.a4	6150i4	\([1, 1, 0, 1525, -35625]\)	\(25076571983/50863698\)	\(-794745281250\)	\([2]\)	\(12288\)	\(0.96786\)