Elliptic curve isogeny class with Cremona label 1936g (LMFDB label 1936.i)

• Label: 1936g
• Number of curves: $3$
• Conductor: $1936$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 1936g have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(11\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(5\)	\( 1 - 3 T + 5 T^{2}\)	1.5.ad
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(13\)	\( 1 + 3 T + 13 T^{2}\)	1.13.d
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 - 5 T + 29 T^{2}\)	1.29.af
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 1936g do not have complex multiplication.

Modular form 1936.2.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 Cremona numbering.

\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)

Isogeny graph

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

Elliptic curves in class 1936g

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
1936.i3	1936g1	\([0, 1, 0, -645, 14771]\)	\(-4096/11\)	\(-79819452416\)	\([]\)	\(960\)	\(0.77937\)	\(\Gamma_0(N)\)-optimal
1936.i2	1936g2	\([0, 1, 0, -20005, -1979309]\)	\(-122023936/161051\)	\(-1168636602822656\)	\([]\)	\(4800\)	\(1.5841\)
1936.i1	1936g3	\([0, 1, 0, -15140165, -22679876749]\)	\(-52893159101157376/11\)	\(-79819452416\)	\([]\)	\(24000\)	\(2.3888\)