Elliptic curve isogeny class with Cremona label 92416v (LMFDB label 92416.bt)

• Label: 92416v
• Number of curves: $2$
• Conductor: $92416$
• CM: \(\Q(\sqrt{-2}) \)
• Rank: $0$

Rank

The elliptic curves in class 92416v have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(19\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(5\)	\( 1 + 4 T + 5 T^{2}\)	1.5.e
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 10 T + 29 T^{2}\)	1.29.k
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

Each elliptic curve in class 92416v has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-2}) \).

Modular form 92416.2.a.v

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 92416v

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
92416.bt2	92416v1	\([0, -1, 0, -1203, -13825]\)	\(8000\)	\(24087491072\)	\([2]\)	\(57024\)	\(0.72167\)	\(\Gamma_0(N)\)-optimal	\(-8\)
92416.bt1	92416v2	\([0, -1, 0, -4813, 115413]\)	\(8000\)	\(1541599428608\)	\([2]\)	\(114048\)	\(1.0682\)		\(-8\)