Elliptic curve isogeny class with Cremona label 11424a (LMFDB label 11424.g)

• Label: 11424a
• Number of curves: $4$
• Conductor: $11424$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 11424a have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(7\)	\(1 - T\)
\(17\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 3 T + 5 T^{2}\)	1.5.d
\(11\)	\( 1 - T + 11 T^{2}\)	1.11.ab
\(13\)	\( 1 + T + 13 T^{2}\)	1.13.b
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 - 2 T + 23 T^{2}\)	1.23.ac
\(29\)	\( 1 - 10 T + 29 T^{2}\)	1.29.ak
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 11424a do not have complex multiplication.

Modular form 11424.2.a.a

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 11424a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
11424.g3	11424a1	\([0, -1, 0, -322, 1960]\)	\(57870788032/10323369\)	\(660695616\)	\([2, 2]\)	\(5376\)	\(0.41170\)	\(\Gamma_0(N)\)-optimal
11424.g2	11424a2	\([0, -1, 0, -1512, -20412]\)	\(747130257224/63241479\)	\(32379637248\)	\([2]\)	\(10752\)	\(0.75828\)
11424.g1	11424a3	\([0, -1, 0, -4912, 134152]\)	\(25604555308424/1102059\)	\(564254208\)	\([2]\)	\(10752\)	\(0.75828\)
11424.g4	11424a4	\([0, -1, 0, 623, 10465]\)	\(6518244032/15785469\)	\(-64657281024\)	\([2]\)	\(10752\)	\(0.75828\)