Elliptic curve isogeny class with Cremona label 97344gr (LMFDB label 97344.f)

• Label: 97344gr
• Number of curves: $2$
• Conductor: $97344$
• CM: \(\Q(\sqrt{-1}) \)
• Rank: $0$

Rank

The elliptic curves in class 97344gr have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 4 T + 5 T^{2}\)	1.5.ae
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(11\)	\( 1 - 2 T + 11 T^{2}\)	1.11.ac
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

Each elliptic curve in class 97344gr has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-1}) \).

Modular form 97344.2.a.gr

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 97344gr

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality	CM discriminant
97344.f2	97344gr1	\([0, 0, 0, 19773, 0]\)	\(1728\)	\(-494763522746688\)	\([2]\)	\(399360\)	\(1.5091\)	\(\Gamma_0(N)\)-optimal	\(-4\)
97344.f1	97344gr2	\([0, 0, 0, -79092, 0]\)	\(1728\)	\(31664865455788032\)	\([2]\)	\(798720\)	\(1.8556\)		\(-4\)