Elliptic curve isogeny class with Cremona label 212160hh (LMFDB label 212160.m)

• Label: 212160hh
• Number of curves: $2$
• Conductor: $212160$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 212160hh have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1 - T\)
\(13\)	\(1 - T\)
\(17\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 - T + 11 T^{2}\)	1.11.ab
\(19\)	\( 1 - 5 T + 19 T^{2}\)	1.19.af
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 + 8 T + 29 T^{2}\)	1.29.i
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 212160hh do not have complex multiplication.

Modular form 212160.2.a.hh

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 212160hh

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
212160.m2	212160hh1	\([0, -1, 0, -1766375341, -47321371853795]\)	\(-595213448747095198927846967296/600281130562949295663181875\)	\(-614687877696460078759098240000\)	\([2]\)	\(247726080\)	\(4.4115\)	\(\Gamma_0(N)\)-optimal
212160.m1	212160hh2	\([0, -1, 0, -33140633841, -2321371551895695]\)	\(245689277968779868090419995701456/93342399137270122585475925\)	\(1529321867465033688440437555200\)	\([2]\)	\(495452160\)	\(4.7581\)