Elliptic curve isogeny class with Cremona label 310206q (LMFDB label 310206.q)

• Label: 310206q
• Number of curves: $2$
• Conductor: $310206$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 310206q have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1 - T\)
\(13\)	\(1 - T\)
\(41\)	\(1 + T\)
\(97\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + T + 5 T^{2}\)	1.5.b
\(7\)	\( 1 - T + 7 T^{2}\)	1.7.ab
\(11\)	\( 1 + 2 T + 11 T^{2}\)	1.11.c
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(19\)	\( 1 + T + 19 T^{2}\)	1.19.b
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 - 9 T + 29 T^{2}\)	1.29.aj
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 310206q do not have complex multiplication.

Modular form 310206.2.a.q

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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 310206q

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
310206.q2	310206q1	\([1, 0, 0, -18645971, 31710685857]\)	\(-716933257039953084158724529/19555843924966303678464\)	\(-19555843924966303678464\)	\([7]\)	\(27176576\)	\(3.0587\)	\(\Gamma_0(N)\)-optimal
310206.q1	310206q2	\([1, 0, 0, -237433631, -4362373486803]\)	\(-1480302302050395483730662419569/7364359653002993324767146804\)	\(-7364359653002993324767146804\)	\([]\)	\(190236032\)	\(4.0316\)