Elliptic curve isogeny class with Cremona label 121275dz (LMFDB label 121275.dn)

• Label: 121275dz
• Number of curves: $3$
• Conductor: $121275$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 121275dz have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1\)
\(5\)	\(1\)
\(7\)	\(1\)
\(11\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + 2 T^{2}\)	1.2.a
\(13\)	\( 1 - T + 13 T^{2}\)	1.13.ab
\(17\)	\( 1 - T + 17 T^{2}\)	1.17.ab
\(19\)	\( 1 + 7 T + 19 T^{2}\)	1.19.h
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 121275dz do not have complex multiplication.

Modular form 121275.2.a.dz

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.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 121275dz

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
121275.dn1	121275dz1	\([0, 0, 1, -984900, 376217406]\)	\(-78843215872/539\)	\(-722311550296875\)	\([]\)	\(1036800\)	\(2.0320\)	\(\Gamma_0(N)\)-optimal
121275.dn2	121275dz2	\([0, 0, 1, -543900, 713858031]\)	\(-13278380032/156590819\)	\(-209846673903798421875\)	\([]\)	\(3110400\)	\(2.5813\)
121275.dn3	121275dz3	\([0, 0, 1, 4858350, -18477635094]\)	\(9463555063808/115539436859\)	\(-154833895655013342796875\)	\([]\)	\(9331200\)	\(3.1306\)