Elliptic curve isogeny class with LMFDB label 7938.g (Cremona label 7938a)

• Label: 7938.g
• Number of curves: $2$
• Conductor: $7938$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 7938.g have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 - 3 T + 23 T^{2}\)	1.23.ad
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 7938.g do not have complex multiplication.

Modular form 7938.2.a.g

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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

Elliptic curves in class 7938.g

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
7938.g1	7938a2	\([1, -1, 0, -8682, -198388]\)	\(23625/8\)	\(24509212865928\)	\([]\)	\(18144\)	\(1.2714\)
7938.g2	7938a1	\([1, -1, 0, -3537, 81843]\)	\(10481625/2\)	\(933897762\)	\([3]\)	\(6048\)	\(0.72211\)	\(\Gamma_0(N)\)-optimal