Elliptic curve isogeny class with Cremona label 129360if (LMFDB label 129360.if)

• Label: 129360if
• Number of curves: $4$
• Conductor: $129360$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 129360if have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1 - T\)
\(7\)	\(1\)
\(11\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 129360if do not have complex multiplication.

Modular form 129360.2.a.if

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 129360if

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
129360.if3	129360if1	\([0, 1, 0, -2025, 45198]\)	\(-488095744/200475\)	\(-377370932400\)	\([2]\)	\(165888\)	\(0.92968\)	\(\Gamma_0(N)\)-optimal
129360.if2	129360if2	\([0, 1, 0, -35100, 2519208]\)	\(158792223184/16335\)	\(491979882240\)	\([2]\)	\(331776\)	\(1.2763\)
129360.if4	129360if3	\([0, 1, 0, 15615, -496350]\)	\(223673040896/187171875\)	\(-352329342750000\)	\([2]\)	\(497664\)	\(1.4790\)
129360.if1	129360if4	\([0, 1, 0, -76260, -4428600]\)	\(1628514404944/664335375\)	\(20008548488544000\)	\([2]\)	\(995328\)	\(1.8256\)