Elliptic curve isogeny class with Cremona label 3150q (LMFDB label 3150.d)

• Label: 3150q
• Number of curves: $2$
• Conductor: $3150$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 3150q have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1\)
\(5\)	\(1\)
\(7\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 8 T + 17 T^{2}\)	1.17.i
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 + 23 T^{2}\)	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 3150q do not have complex multiplication.

Modular form 3150.2.a.q

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.

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

Isogeny graph

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

Elliptic curves in class 3150q

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
3150.d1	3150q1	\([1, -1, 0, -18117, -108459]\)	\(461889917/263424\)	\(375070500000000\)	\([2]\)	\(15360\)	\(1.4863\)	\(\Gamma_0(N)\)-optimal
3150.d2	3150q2	\([1, -1, 0, 71883, -918459]\)	\(28849701763/16941456\)	\(-24121721531250000\)	\([2]\)	\(30720\)	\(1.8329\)