Elliptic curve isogeny class with Cremona label 1260b (LMFDB label 1260.d)

• Label: 1260b
• Number of curves: $4$
• Conductor: $1260$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 1260b have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 6 T + 19 T^{2}\)	1.19.g
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 1260b do not have complex multiplication.

Modular form 1260.2.a.b

Isogeny matrix

The \((i,j)\)-th 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, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 1260b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
1260.d4	1260b1	\([0, 0, 0, -348, 2497]\)	\(10788913152/8575\)	\(3704400\)	\([6]\)	\(288\)	\(0.19075\)	\(\Gamma_0(N)\)-optimal
1260.d3	1260b2	\([0, 0, 0, -423, 1342]\)	\(1210991472/588245\)	\(4065949440\)	\([6]\)	\(576\)	\(0.53732\)
1260.d2	1260b3	\([0, 0, 0, -1188, -12987]\)	\(588791808/109375\)	\(34445250000\)	\([2]\)	\(864\)	\(0.74005\)
1260.d1	1260b4	\([0, 0, 0, -18063, -934362]\)	\(129348709488/6125\)	\(30862944000\)	\([2]\)	\(1728\)	\(1.0866\)