Elliptic curve isogeny class with LMFDB label 309168.d (Cremona label 309168d)

• Label: 309168.d
• Number of curves: $2$
• Conductor: $309168$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 309168.d have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(19\)	\(1 + T\)
\(113\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 4 T + 5 T^{2}\)	1.5.e
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 309168.d do not have complex multiplication.

Modular form 309168.2.a.d

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 309168.d

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
309168.d1	309168d1	\([0, 0, 0, -71263227, -136593274070]\)	\(13403946614821979039929/5057590268826067968\)	\(15101883621270337735360512\)	\([2]\)	\(121405440\)	\(3.5310\)	\(\Gamma_0(N)\)-optimal
309168.d2	309168d2	\([0, 0, 0, 222934533, -974762692310]\)	\(410363075617640914325831/374944243169850027552\)	\(-1119577510997281464669831168\)	\([2]\)	\(242810880\)	\(3.8775\)